Equation of a Line Test

Result

Equation of a Line Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

In a triangle ABC, the coordinates of vertex A are (1, 8), and the midpoints of the sides AB and AC are (4, 10) and (- 1, 12). What is the equation of median passing through the vertex A?

A
y = 3x + 5

B
y = 6x + 2

C
y = 4x + 4

D
y = x + 7

E
y = 8x
Question 2
1 / -0

If the roots of the equation are m₁ and m₂ (m₁> m₂), what is the equation of line passing through (1, 6) and point of intersection of the lines y = m₁x - 3 and y = m₂x + 8?

A
43x - 6y = 0

B
43x - 6y = 7

C
43x - 6y = 10

D
6y - 43x = 10

E
6y - 43x = 7
Question 3
1 / -0

The vertices of a triangle ABC are (- 3, - 5), (3, 8) and (0, 12) taken in order. Then, the equation of the line passing through B and parallel to the median passing through A is

A
2x - 3y = 6

B
10x - 3y = 6

C
3y - 10x = 6

D
10x - y = 6

E
10x - 3y = 10
Question 4
1 / -0

One of the possible equations of the lines passing through the point (- 1, 1) and making an intercept of length units between the lines y = 2x and y = 3 x is

A
y = 3x + 4

B
y = 3x + 2

C
y = 4x + 5

D
y = x + 2

E
y = 2x + 3
Question 5
1 / -0

One end of the unstretched elastic string is placed at (0, 0) and the other end at (3, 5). On stretching it to the triple of its original length, it reaches the point A. Then, the equation of the line passing through A and perpendicular to the string is

A
5y - 3x = 102

B
3y - 5x = 102

C
5y + 3x = 102

D
3y + 5x = 102

E
y + 3x = 102
Question 6
1 / -0

A line makes positive intercepts on both the axes such that the ratio between X intercept and Y intercept is 2 : 3. If it passes through (1, 2), the equation of the line is

A
3x - 2y = 7

B
3x + 2y = 7

C
2x + 3y = 7

D
3y + 4x = 7

E
3x + 4y = 7
Question 7
1 / -0

Three of the vertices of a parallelogram ABCD are A (a, b), B (b, a) and C (- b, a). Then, the equation of the side AD is

A
y + b = 0

B
y - a = 0

C
y + a = 0

D
y - b = 0

E
y + a = b
Question 8
1 / -0

The equation of sides of a parallelogram are 2x + y = 4 and 2x - y = - 4. If two of the vertices of the parallelogram are (2, 0) and (0, - 4), the equation of the diagonal passing through (0, - 4) is

A
y = 2

B
x = 0

C
y = 0

D
x = 2

E
y = 5
Question 9
1 / -0

A straight line passes through A (3, 2) and has a slope of . Then, the coordinates of the points on the line, which are at the distance of 5 units from A are

A
(- 1, - 1) and (7, - 5)

B
(- 1, 1) and (7, 5)

C
(- 1, - 1) and (7, 5)

D
(- 1, - 1) and (- 7, 5)

E
(1, 1) and (7, 5)
Question 10
1 / -0

A line is drawn through a point P (a, b) such that it meets the line at Q and PQ =. Find the equation of the line PQ.

A

B
ax = by

C
ay = b (x + a)

D
y = ax + b

E
ax = by + a
Question 11
1 / -0

A parallelogram ABCD has vertices A (- 3, - 5), B (3, - 5) and D (- 1, 7). Then, the equation of the diagonal AC is

A
6x + 5y = 7

B
5x + 6y = 7

C
6x + 5y = 11

D
6x - 5y = 7

E
5y - 6x = 7
Question 12
1 / -0

The shortest distance between point (8, - 6) and line y = is

A

B

C

D

E