# Reflection of a Point about a Line

## Trending Questions

**Q.**A ray of light coming from the point (2, 2√3) is incident at an angle 30∘ on the line x=1 at the point A. The ray gets reflected on the line x=1 and meets X−axis at the point B. Then, the line AB passes through the point:

- (4, −√3)
- (3, −1√3)
- (3, −√3)
- (4, −√32)

**Q.**A ray of light along x+√3y=√3 gets reflected upon reaching X-axis, the equation of the reflected ray is

- y=√3x−√3
- y=x+√3
- √3y=x−√3
- √3y=x−1

**Q.**The point P(a, b) undergoes the following three transformations successively :

(a) Reflection about the line y=x.

(b) Translation through 2 units along the positive direction of x−axis.

(c) Rotation through angle π4 about the origin in the anti-clockwise direction.

If the co-ordinates of the final position of the point P are (−1√2, 7√2), then the value of 2a+b is equal to

- 9
- 5
- 13
- 7

**Q.**The point (4, 1) undergoes the following three transformations succesively.

(i) Image about the line y=x

(ii) Transformation through a distance 2 unit along the positive direction of x axis

(iii) Rotation through an angle of π4 about the origin in the anti-clockwise direction.

The final position of the point is given by the coordinates

- (1√2, 7√2)
- (−2, 7√2)
- (−1√2, 7√2)
- (√2, 7√2)

**Q.**The reflection of the point (4, -13) in the line 5x+y+6=0 is

- (-1, -14)
- (3, 4)
- (1, 2)
- (-4, 13)

**Q.**A line from origin meets the line (x-2)/1 = (y-1)/-2 = (z+1)/1 and (x-8/3)/2 = ( y+3)/1 = (z-1)/1 at P and Q respectively. Find the distance PQ

**Q.**

If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.

**Q.**For an equilateral triangle, one side lies on x+y=6 and the 3rd vertex is mirror image of the origin in the mirror x+y=6. Then the coordinates of other two vertices are

- (3+√3, 3−√3)
- (3+√3, 3+√3)
- (3−√3, 3+√3)
- (3−√3, 3−√3)

**Q.**A straight line cuts the x-axis at point A(1, 0) and y-axis at point B, such that ∠OAB=α, (α>π/4).

C is the middle point of AB. If B′ is the mirror image of B with respect to line OC and C′ is a mirror image of point C with respect to line BB′, then the ratio of the areas of triangle ABB′ and BB′C′ is

**Q.**The point (4, 1)undergoes the following two successive transformation

(i) Reflection about the line y=x

(ii) Translation through a distance 2 units along the positive x-axis

Then the final coordinates of the point are

- (4, 3)
- (3, 4)
- (1, 4)
- (72, 72)

**Q.**Statement 1: If P1(x1, y1) and P2(x2, y2) be the images of point P(x, y) about lines L1≡ax+by+c and L2≡bx−ay+c′=0 respectively, then the line joining points P1 and P2 always passes through point of intersection of lines L1 and L2

Statement 2: Lines L1 and L2 are perpendicular

- Statement 1 is true, statement 2 is false
- Statement 1 is false, statement 2 is true
- Statement 1 is true, statement 2 is also true; statement 2 is the correct explanation of statement 1
- Statement 1 is true, statement 2 is also true; statement 2 is not the correct explanation of statement 1

**Q.**

Find the image of the point (2, 1) with respect to the line mirror x+y−5=0.

**Q.**The image of the point P(3, 5) with respect to the line y=x is the point Q and the image of Q with respect to the line y=0 is the point R(a, b), then (a, b) is equal to

- (5, 3)
- (5, −3)
- (−5, 3)
- (−5, −3)

**Q.**A ray of light emerging from the point source placed at P(1, 2) is reflected at a point Q on the y-axis and then passes through the point (6, 9). Then

- Q≡(0, 3)
- image of P in y−axis is (−1, 2)
- equation of incident ray is x+y=3
- equation of reflected ray is y=x+3

**Q.**

The equation of the straight line passing through the point (2, –2) and the point of intersection of the lines 5x – y = 9 and x + 6y = 8 is

y – 2 = 0

y + 2 = 0

x + 2 = 0

x – 2 = 0

**Q.**If the image of the point P(4, −13) with respect to the line 5x+y+6=0 is Q, then the area of the triangle formed by the line through Q, which makes equal intercepts on the coordinate axes, with the coordinate axes, can be

- 72 sq. units
- 84.5 sq. units
- 112.5 sq. units
- 128 sq. units

**Q.**

Statement I: The point $A(3,1,6)$ is the mirror image of the point $P(1,3,4)$ in the plane $x-y+z=5$.

Statement II: The plane $x-y+z=5$ bisects the line segment joining $A(3,1,6)$ and $B(1,3,4)$ .

Statement I is correct, Statement II is correct; Statement II is the correct explanation for Statement I

Statement I is correct, Statement II is correct; Statement II is not the correct explanation for Statement I

Statement I is correct, Statement II is incorrect

Statement I is incorrect, Statement II is correct

**Q.**The image of the point (−8, 12) with respect to the line mirror 4x+7y+13=0 is

- (−16, 2)
- (16, −2)
- (−16, −2)
- (−2, −16)

**Q.**A beam of light ray sent along the line x−y=1 , which after refracting from x axis enters the opposite side by turning through 30o away from the normal at the point of incidence with x axis. then which of the following options are correct ?

- Y− intercept of refracted ray is 2−√3
- Y− intercept of refracted ray is √3−2
- perpendicular distance from origin to refracted ray is √3+12√2 units
- perpendicular distance from origin to refracted ray is √3−12√2 units

**Q.**If the mirror image of point (1, 2) in the line 2y=x is (a, b), then the value of 5(a+b) is:

**Q.**The image of the point P(4, 1) with respect to the line y=x-1 is

- (2, 3)
- (2, -3)
- (-2, -3)
- (-2, 3)

**Q.**Locus of image of the point P(h, k) with respect to the line mirror which passes through the origin is

- x2+y2=hx+ky
- x2+y2=h2+k2
- x2+y2=h2+hx
- x2+y2=h2+k2+hx+ky

**Q.**If a ray of light passing through (2, 2) reflects on the x−axis at a point P and the reflected ray passes through the point (6, 5), then the co-ordinates P is

- (137, 0)
- (277, 0)
- (227, 0)
- (257, 0)

**Q.**If the point A is symmetric to the point B(4, −1) with respect to the bisector of the first quadrant, then the length of AB is

- 5 units
- 5√2 units
- 3√2 units
- 3 units

**Q.**If the square ABCD where A(0, 0), B(2, 0), C(2, 2) and D(0, 2) undergoes the following transformations successively

(i) image with respect to line y=x

(ii) f2(x, y)→(x+3y, y)

(iii) f3(x, y)→(x−y2, x+y2), then the final figure formed by the transformed vertices is

- square
- parallelogram
- rhombus
- None of these

**Q.**

The reflection of the point (4, -13) about the line 5x+y+6=0 is

(-1, -14)

(0, 0)

(3, 4)

(1, 2)

**Q.**

Write the coordinates of the imeage of the point (3, 8) in the line x+3y−7=0.

**Q.**The image of the point P(4, −13) in the line mirror 5x+y+6=0, is

- (1, −14)
- (6, −15)
- none of these
- (−1, −14)

**Q.**If a ray of light passing through (2, 2) reflects on the x−axis at a point P and the reflected ray passes through the point (6, 5), then the co-ordinates P is

- (137, 0)
- (227, 0)
- (257, 0)
- (277, 0)

**Q.**The equation of the line passing through the points (1, –2, 3) and parallel to the planes x−y+2z−5=0 and 3x+y+z−6=0 is

- x−1−3=y+25=z−34
- x−11=y+2−1=z−32
- x−13=y+25=z−3−4
- x−11=y+21=z−32