Question

a line intersects the y axis and x axis at the point P and Q respectively if (2, - 5) is a midpoint of PQ then find the coordinates of P and Q

Answer 1

We have midpoint formula for a line x=(x1+x2)/2 and y=(y1+y2)/2.
so here x=2 and y=-5
As P intersects y-axis so its x-component is 0 and Q intersects x-axis hence its y-component is 0. That gives us P=(0,y1) and Q=(x2,0)
Using mid point formula,
2=(0+x2)/2
therefore, x2= 4
And, -5=(y1+0)/2
therefore, y1= -10

Hence the answer is P(0,-10) and Q(4,0).

Answer 2

Given P= (0,y)
Q= (x, 0)

$x1 + x2 \div 2 \\ y1 + y2 \div 2$
let P=(0, y) be x1 and y1
let Q= ( x, 0) be x2 and y2

Given (2,-5) as x, y
2=0+x/2
4=0+x
x1=4

-5=y+0/2
-10=y+0
y1=-10

P= (0,-10)
Q=(4,0)