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Question 41 .
Chap: Coordinate Geometry Class 10.

Answer 1

x-4y-6 = 0

Express in the form of y=mx+c, where m is the slope

x-4y-6=0

-4y = -x+6

y=1/4 x - 3/2

When two lines are perpendicular, the product of their slope =  -1

Slope of the given line = 1/4

Let slope of PQ =  m2

1/4 x m2 = -1

m2= -4

Let (x, y) be a general point on PQ

Using this point to get the equation of PQ, since we know the slope of PQ

(y-3)/(x-1) = -4

y-3 = -4(x-1)

y-3 = -4x - 4

y = -4x -1

The mid-point is the point of intersection of the two lines:

So, at that point

1/4 x - 3/2 = -4x -1

1/4x + 4x = -1 + 3/2

4  1/4 x = 1/2

x = 2/17

y= -4x -1 = -4(2/17) - 1

y = -1  8/17

The mid-point is (2/17,  -1 8/17)

Let point Q be (a , b)

Getting the mid-point using point P

mid-point = {(a+1)/2  , (b+3)/2} = (2/17,  -1 8/17)

⇒(a+1)/2 = 2/17

a+1 = 2 x 2/17 = 4/17

a = -13/17

⇒ (b+3)/2 = -1  8/17

b+3 = -2  16/17

b= -5  16/17

So Q is (-13/17,  -5 16/17)

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Answer 2

hey mate
here's the solution