Question

if the image of the point (2,3) with respect to a line L=0is (-4,1)then find its foot of the perpendicular​

Answer 1

Explanation:

Mid point of P(2,3) & Q(4,5)

= 22+4,23+5=(3,4)

Slope of PQ=1

slope of line L= -1

(3,4) lies on L

∴ equation of L.

y−4=−1(x−2)

⇒x+y−7=0⋯(1)

Let image of R(0,0) be S(x1,y1)

mid point of RS=(2x1,2y1) which lies on (1)

x1+y1=14

slope of RS=x1y1

As RS⊥ line L

∴x1y1×(−1)=−1

∴x1=y1

So, x1=y1=7 Thus R S = (7,7)