Question

consider the line segment joining P=(3,-4) and Q=(4,4). Find the coordinates of R if R is a point on the y-axis and /_PRQ=90 degrees. Need help please

Answer 1

Since Angle PRQ is 90 degrees,, the basic rules of geometry states that
linear line PR is perpendicular to linear line RQ.
This means the gradient of PR *the gradient of RQ = -1
Let the coordinate of R be (x,y).
Since R is a point on the y-axis, y = 0
So the coordinate of R we assume is R(x,0)

Answer 2

So we have this equation:
For two points (x1,y1),(x2,y2),the general formula of gradient between the two points are
(y2-y1)/(x2-x1)
So we have:
the gradient of PR = (-4-0)/(3-x)
the gradient of RQ = (4-0)/(4-x)
so their product is -1. You may solve this equation and find out x, which is the x-coordinate of R.

Answer 3

Isn't it supposed to be x=0??

Answer 4

An, you are right. A careless mistake. x = 0. So let R be (0,y)
Same procedure

Answer 5

okay thanks a lot.