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# ISI MStat 2019 PSA Problem 14 | Reflection of a point

This is a problem from ISI MStat 2019 PSA Problem 14. First, try the problem yourself, then go through the sequential hints we provide.

## Reflection of a point - ISI MStat Year 2019 PSA Question 14

The reflection of the point (1,2) with respect to the line $$x+2 y=15$$ is

• (3,6)
• (6,3)
• (10,5)
• (5,10)

### Key Concepts

Straight line

ISI MStat 2019 PSA Problem 14

Precollege Mathematics

## Try with Hints

Find an algorithm to find the reflection,

Find the line perpendicular to $$x+2 y=15$$ through (1,2).
Find the point of intersection.
Use Midpoint Segment Result.

The line perpendicular to $$x+2 y=15$$ is of the form $$-2x+y=k$$ .Now it passes through (1,2) . So, $$-2+2=k \Rightarrow k=0$$

Hence the line perpendicular to $$x+2 y=15$$ through (1,2) is y=2x.

Now we will find point of intersection (Foot of Perpendicular )

(3,6) is the point of intersection i.e the foot of perpendicular.

Use Mid-Point Formula (special case of Section formula) to get required point (Foot of perpendicular is mid-point of reflection and original point)

$$(3,6)=( \frac{x+1}{2} , \frac{y+2}{2} )$$ $$\Rightarrow x=5 , y=10$$

Therefore the reflection point is (5,10) .