Pair of Straight Lines Test

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Pair of Straight Lines Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The image of the point (α,β) with respect to the line x + y = 0 is

1. ( - β,−α)

2. (α,β)

3. none of these

4.(β,α)

A
1 and 2

B
3 and 4

C
1 and 3

D
3 and 4

Solution

The equation of the line which is perpendicular to the given line x+y=0 is x - y =0

The point of intersection of these two lines is (0,0) which is the origin

This point of intersection is the midpoint of the given point (α,β) and its image, say (a,b)

Therefore α+a2

This implies a = −α

Similarly β+b2 = 0

This implies b = −β

Therefore (−α,−β) is the image
Question 2
1 / -0

Slope of any line parallel to X axis is

A
0

B
1

C
-1

D
none of these

Solution

Since the angle made with x axis is zero, since tanθ is the slope. Then tan0 = 0

Hence the slpoe of the line parallel to X-axis is zero
Question 3
1 / -0

The vertices of a triangle are (0, 0), (3, 0) and (0, 4). Its orthocentre is at

A
(0, 0)

B
(1, 4/3)

C
(3/2, 2)

D
None of these
Question 4
1 / -0

The image of the point (α,β) with respect to the line x = y is

A
(α,β)

B
( - α,−β)

C
( - β,−α)

D
(β,α)
Question 5
1 / -0

The equation of the line passing through the points (2, 3) and making an intercept of length 2 units between the lines y + 2x = 3 and y + 2x = 5 is

A
x + 3 = 0

B
y – 2 = 0

C
x – 2 = 0

D
None of these
Question 6
1 / -0

The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0

1. 2

2. none of these

3. - 2

4. 8

A
1 and 2

B
2 and 3

C
1 and 4

D
4 and 1
Question 7
1 / -0

The straight lines x + y = 0, 3x + y − 4 = 0 and x + 3y − 4 = 0 form which of the following triangles?

A
Isosceles

B
Equilateral

C
Right-angled

D
None of these
Question 8
1 / -0

Slope of a line is not defined if the line is

A
parallel to Y axis

B
parallel to the line x – y

C
parallel to the line x+y

D
parallel to X axis

Solution

Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.
Question 9
1 / -0

If P(1, 0), Q(– 1, 0) and R(2, 0) are three given points, then the locus of point S, which satisfies the relation (SQ)² + (SR)² = 2(SP)², is (where SQ, SR and SP are line segments)

A
a straight line || to x-axis

B
a circle through the origin

C
a circle with centre at the origin

D
a straight line || to y-axis

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Re-Attempt Weekly Quiz Competition

Pair of Straight Lines Test - 1

Result

Pair of Straight Lines Test - 1

Score

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Rank

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SHARING IS CARING

Question 1

1 and 2

3 and 4

1 and 3

3 and 4

Solution

Question 2

0

1

-1

none of these

Solution

Question 3

(0, 0)

(1, 4/3)

(3/2, 2)

None of these

Question 4

(α,β)

( - α,−β)

( - β,−α)

(β,α)

Question 5

x + 3 = 0

y – 2 = 0

x – 2 = 0

None of these

Question 6

1 and 2

2 and 3

1 and 4

4 and 1

Question 7

Isosceles

Equilateral

Right-angled

None of these

Question 8

parallel to Y axis

parallel to the line x – y

parallel to the line x+y

parallel to X axis

Solution

Question 9

a straight line || to x-axis

a circle through the origin

a circle with centre at the origin

a straight line || to y-axis

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