Coordinate Geometry Test

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Coordinate Geometry Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

At what point does the line y = 5x + 7 cut the y-axis?

A
(7, 0)

B
(0, 7)

C
(0, 10)

D
(10, 0)

Solution

To cut the y-axis , the value of x should be 0.
Put x = 0 in the given equation.
y = 5x + 7
y = 5(0) + 7
y = 7
So, it cuts the y-axis at point (0, 7).
Question 2
1 / -0

The point (-3, 6) belongs to the line

A
4y = 3x + 23

B
3y = 2x + 24

C
2y = x + 25

D
y = 2x + 26

Solution

If the point (-3 , 6) lies on the line, it will satisfy its equation.

1) 4y = 3x + 23
x = -3, y = 6
4 × 6 = 3 × (-3) + 23
24 ≠ -9 + 23
Hence, option 1 is incorrect.

2) 3y = 2x + 24
x = -3, y = 6
3y = 2x + 24
3(6) = 2(-3) + 24
18 = -6 + 24
18 = 18
The given point belongs to the line 3y = 2x + 24.

Hence, option 2 is the correct answer.
Question 3
1 / -0

Find out the point which lies on the line 6x = 2y + 4.

A
(3, 6)

B
(3, 7)

C
(3, 8)

D
(3, 9)

Solution

1) Points (3, 6)
6x = 2y + 4
6 × 3 = 2 × 6 + 4
18 ≠ 12 + 4
Hence, option 1 is incorrect

2) Points (3, 7)
6x = 2y + 4
6(3) = 2(7) + 4
18 = 14 + 4
18 = 18
Hence, option 2 is the correct answer.
Question 4
1 / -0

In which quadrants do the points (-5, 2) and (5, -5) lie?

A
1^stand 4^th quadrants, respectively

B
2^nd and 4^th quadrants, respectively

C
2^nd and 3^rdquadrants, respectively

D
4^th and 2^nd quadrants, respectively

Solution

As shown, the given points (-5,2) and (5,-5) lie in the 2^nd and 4^th quadrants, respectively.
Question 5
1 / -0

If a = 3, b = –4 and c = 2, then (a + b, b + c) will lie in the

A
1^st quadrant

B
2^nd quadrant

C
3^rd quadrant

D
4^th quadrant

Solution

a = 3, b = –4, c = 2
a + b = 3 + (–4) = 3 – 4 = –1
b + c = –4 + 2 = –2
Now, (a + b) is the abscissa and is negative.
Also, (b + c) is the ordinate and is negative.
Since both abscissa and ordinate are negative, (a + b, b + c) will lie in the 3^rd quadrant.
Question 6
1 / -0

The coordinates of a point are (x + 3, y - 7). Find the sum of x and y if the coordinates of the same point are (5, 8).

A
16

B
17

C
19

D
21

Solution

Equating the coordinates:
x + 3 = 5 and y – 7 = 8
x = 5 - 3 = 2
y = 8 + 7 = 15
Now, x + y = 2 + 15 = 17
Question 7
1 / -0

Find the value of 'y' in the ordered pair (2, y) if the abscissa is 5 less than the ordinate.

A
-7

B
7

C
5

D
-3

Solution

Abscissa = 2
Ordinate = y
According to the question:
2 = y – 5
y = 7
Question 8
1 / -0

What will be the coordinates of point P, if its ordinate is same as the abscissa of (3, 0) and its abscissa is same as the ordinate of (9, 2)?

A
(3, 2)

B
(2, 3)

C
(9, 3)

D
(9, 0)

Solution

Ordinate of point P = abscissa of (3, 0)
= 3
Abscissa of Point P = ordinate of (9, 2)
= 2
Co - ordinates of point P = (2, 3)
Question 9
1 / -0

The 'x' and 'y' coordinates of a point are called _________ and __________, respectively.

A
abscissa; origin

B
abscissa; ordinate

C
abscissa; quadrant

D
ordinate; abscissa

Solution

The distance of a point from the y-axis is called its x-coordinate, or abscissa.
The distance of a point from the x-axis is called its y-coordinate, or ordinate.
The 'x' and 'y' coordinates of a point are called abscissa and ordinate, respectively.
Question 10
1 / -0

The sum of abscissas of two points is -2. Which of the following can be the possible set of points?

A
A(1, -2); B(3, 4)

B
A(1, 2); B(-3, -4)

C
A(-1, -2); B(-3, 4)

D
A(-1, 2); B(3, -4)

Solution

Option 1:

A(1, -2); B(3, 4)
Abscissa of A = 1
Abscissa of B = 3
Sum = 1 + 3 = 4
Hence, option 1 is incorrect.

Option 2:

A(1, 2); B(-3, -4)

Abscissa of A = 1
Abscissa of B = -3
Sum = -3 + 1 = -2

Thus, this is the correct answer.
Question 11
1 / -0

What is the distance of point (-3, -4) from the x-axis?

A
1 unit

B
3 units

C
4 units

D
7 units

Solution

The vertical distance of point (-3, -4) from the x-axis is 4 units.
Question 12
1 / -0

Which of the following points lies on y-axis?

A
(-2, -3)

B
(0, 3)

C
(-3, 0)

D
(-5, 4)

Solution

Point (0, 3) lies on y-axis as its x-coordinate is zero.
Question 13
1 / -0

Directions For Questions

Directions: Study the following graph and answer the question that follows.

...view full instructions

The abscissa and ordinate of point A are

A
(-3, 2)

B
(-3, -2)

C
(3, 2)

D
(-2, 3)

Solution

The abscissa is the point on X-axis.
The ordinate is the point on Y-axis.
Thus, according to the given grid, the abscissa of point A is -3, and the ordinate is 2.
Therefore, the co-ordinate point is (-3, 2).
Question 14
1 / -0

Directions For Questions

Directions: Study the following graph and answer the question that follows.

...view full instructions

(Ordinate of point C) - (Abscissa of point A) = _________

A
-1

B
2

C
4

D
-5

Solution

The co-ordinates of point of A are (-3, 2). The abscissa of point A is -3.
The co-ordinates of point C are (-2, -4). The ordinate of point C is -4.
Thus,
(Ordinate of C) - (Abscissa of point A) = -4 - (-3) = -4 + 3 = -1
Question 15
1 / -0

Directions For Questions

Directions: Study the following graph and answer the question that follows.

...view full instructions

The sum of ordinates of points A, B, C, and D is ______.

A
0

B
2

C
1

D
3

Solution

The co-ordinates of point A are (-3, 2). The ordinate of point A is 2.
The co-ordinates of point B are (4, 4). The ordinate of point B is 4.
The co-ordinates of point C are (-2, -4). The ordinate of point C is -4.
The co-ordinates of point D are (3, 0). The ordinate of point D is 0.
The required sum = 2 + 4 + (-4) + 0 = 2
Question 16
1 / -0

Directions: Study the following graph and answer the question that follows.

Abscissa of point W - Abscissa of point U = _______

A
1

B
2

C
3

D
4

Solution

Coordinates of point U and W are (3, 5) and (4, -1) respectively.
Required difference between abscissa = 4 – 3 = 1
Question 17
1 / -0

The area of the rectangle formed by joining points A(3, 4), B(6, 4), C(6, 2) and D(3, 2) is ________.

A
6 sq. units

B
7 sq. units

C
8 sq. units

D
10 sq. units

Solution

AB = 6 - 3 = 3 units
BC = 4 - 2 = 2 units
Area of rectangle = AB × BC
= 3 × 2
= 6 sq. units
Question 18
1 / -0

The perpendicular distance of point (2, -5) from y-axis is ________.

A
2 units

B
4 units

C
5 units

D
6 units

Solution

Perpendicular distance of (2, -5) from y-axis is 2 units.
Question 19
1 / -0

If the distance of a point P from the negative x-axis is 3 units and that from the positive y-axis is 2 units, then in which of the following quadrants must the point lie?

A
I

B
II

C
III

D
IV

Solution

Point P must lie in quadrant II.
Question 20
1 / -0

Point X lies in the second quadrant and point Y lies in the third quadrant. Signs of abscissa of point X and point Y, respectively are _____.

A
+ and +

B
+ and -

C
- and -

D
- and +

Solution

Sign of abscissa in the second quadrant = -
Sign of abscissa in the third quadrant = -
Therefore, (- and -) is the correct option.
Question 21
1 / -0

State T for true and F for false for the following statements and choose the suitable option from the given table.

(i) The coordinates of a point are of the form (+, +) in the first quadrant, (-, +) in the second quadrant, (-, -) in the third quadrant, and (+, -) in the fourth quadrant, where "+" denotes a positive real number and "-" denotes a negative real number.
(ii) The coordinates of the origin are (0, 0).
(iii) The coordinates of a point on the x-axis are of the form (x, 0) and those of the point on the y-axis are (y, 0).
(iv) If abscissa of a point is 2 and the ordinate is 2, then the point lies in the first quadrant.

A
D

B
C

C
B

D
A

Solution

(i) The coordinates of a point are of the form (+, +) in the first quadrant, (-, +) in the second quadrant, (-, -) in the third quadrant, and (+, -) in the fourth quadrant, where "+" denotes a positive real number and "-" denotes a negative real number.

(ii) The coordinates of the origin are (0, 0).

(iii) The coordinates of a point on the x-axis are of the form (x, 0) and those of the point on the y-axis are (0, y). So, this statement is false.

(iv) If abscissa of a point is 2 and the ordinate is 2, then the point lies in the first quadrant. So, this statement is true.
Question 22
1 / -0

Fill in the blanks.

(I) The point 3 places below (2, 1) is in the _____________.
(II) All the coordinates are _________________ in the 3rd quadrant.
(III) A man in a car started from origin, goes towards east for 120 km and then goes towards north for 150 km. He then takes a turn towards south, and goes 200 km, after which he goes towards west for 180 km. The man is in the ________ quadrant now. (Take 1 km = 1 unit)
(IV) If a mirror is placed on the y axis, then the coordinates of the mirror image of point (-3, 9) will be ______.

A
4^th quadrant, positive, 3^rd, (3,-9)

B
4^th quadrant, negative, 3^rd, (3, 9)

C
3^rd quadrant, negative, 4^th, (3, -9)

D
4^th quadrant, negative, 4^th, (3, 9)

Solution

(I)
Here we can see that the point now lies in the 4th quadrant.
(II)
From this figure it can be seen that all the points in the 3rd quadrant are negative.

(III) A man in a car starts from origin towards east and drives for 120 km. The man is still on x-axis. Then he drives towards north for 150 km (which means the first quadrant). Then he starts moving towards south and drives for 200 km, which means that the man has gone 50 km down in the 4th quadrant.
After that he drives towards west for 180 km. At the end, the man is in 3rd quadrant.

In the figure, O is the starting point.

(IV)

Here it can be seen that in mirror image, the points will be (3, 9).
Question 23
1 / -0

The figure given above is rectangle HIJK and the sides HI and IJ are parallel to X-axis and Y-axis, respectively. HI = 10 units and IJ = 6 units. Also, the centre of the rectangle is at the origin. If we put a point L, 2 spaces right and 3 spaces above I, find:

(I) Product of the abscissa of K and the ordinate of L
(II) One less than the sum of the abscissas of H and L, and the ordinate of K

A
A

B
B

C
C

D
D

Solution

(i) Abscissa of K = -5
Ordinate of L = 6
Therefore, required product = -5 × 6 = -30
(ii) Abscissa of H = -5
Ordinate of K = -3
Abscissa of L = 7
Therefore, required sum = (-5) + (-3) + 7 = -1
1 less than -1 is -2.
Question 24
1 / -0

HIJK is a quadrilateral with centre at origin. The measurements of the quadrilateral are given in the figure in units, where HI = IJ = JK = KH. Find the coordinates of all the vertices of the quadrilateral.

A
H = (0, 2u), I = (3v, 0), J = (0, -2u), K = (-3v, 0)

B
H = (2v, 0), I = (2u, 0), J = (0, -2u), K = (-3v, 0)

C
H = (0, 3v), I = (3u, 0), J = (1, -2u), K = (-3v, 0)

D
H = (3v, 0), I = (0, 4u), J = (0, 3u), K = (-2v, 0)

Solution

Question 25

1 / -0

Choose the correct option:

(P)	The area of triangle △OPR with vertices O(0, 0), P(0, 6) and R(5, 0)
(Q)	The area of rectangle PSRQ with vertices P(10, 0), Q(14, 0), R(14, 8) and S(10, 8)
(R)	The area of square ABCD with vertices A(5, 5), B(10, 5), C(10, 0) and D(5, 0)

(A) P = 15 sq. units, Q = 11 sq. units, R = 25 sq. units
(B) P = 15 sq. units, Q = 32 sq. units, R = 25 sq. units
(C) P = 17 sq. units, Q = 32 sq. units, R = 26 sq. units
(D) P = 14 sq. units, Q = 25 sq. units, R = 25 sq. units

A

B

C

D

Solution

(P)

The area of triangle △OPR with vertices O(0, 0), P(0, 6) and R(5, 0)
=

= × 6 × 5 = 15 sq. units

(Q)

Area of rectangle PSRQ wtih vertices P(10, 0), Q(14, 0), R(14, 8) and S(10, 8) = PQ × QR = 4 × 8 = 32 sq. units

(R)

Area of square ABCD with vertices A(5, 5), B(10, 5), C(10, 0) and D(5, 0) = AB × BC = 5 × 5 = 25 sq. units

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Coordinate Geometry Test - 7

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Coordinate Geometry Test - 7

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Question 1

(7, 0)

(0, 7)

(0, 10)

(10, 0)

Solution

Question 2

4y = 3x + 23

3y = 2x + 24

2y = x + 25

y = 2x + 26

Solution

Question 3

(3, 6)

(3, 7)

(3, 8)

(3, 9)

Solution

Question 4

1st and 4th quadrants, respectively

2nd and 4th quadrants, respectively

2nd and 3rd quadrants, respectively

4th and 2nd quadrants, respectively

Solution

Question 5

1st quadrant

2nd quadrant

3rd quadrant

4th quadrant

Solution

Question 6

16

17

19

21

Solution

Question 7

-7

7

5

-3

Solution

Question 8

(3, 2)

(2, 3)

(9, 3)

(9, 0)

Solution

Question 9

abscissa; origin

abscissa; ordinate

abscissa; quadrant

ordinate; abscissa

Solution

Question 10

A(1, -2); B(3, 4)

A(1, 2); B(-3, -4)

A(-1, -2); B(-3, 4)

A(-1, 2); B(3, -4)

Solution

Question 11

1 unit

3 units

4 units

7 units

Solution

Question 12

(-2, -3)

(0, 3)

(-3, 0)

(-5, 4)

Solution

1^stand 4^th quadrants, respectively

2^nd and 4^th quadrants, respectively

2^nd and 3^rdquadrants, respectively

4^th and 2^nd quadrants, respectively

1^st quadrant

2^nd quadrant

3^rd quadrant

4^th quadrant

4^th quadrant, positive, 3^rd, (3,-9)

4^th quadrant, negative, 3^rd, (3, 9)

3^rd quadrant, negative, 4^th, (3, -9)

4^th quadrant, negative, 4^th, (3, 9)