Question

The line x + y - 6= 0 is the right bisector

Answer 1

Answer:

Therefore, the coordinates of point Q is (2,3)

Step-by-step explanation:

Let the coordinates of Q be(a,b)

Let R be the midpoint of PQ

Coordinates of R $=(\frac{4+a}{2}, \frac{3+b}{2})$

R lies on the line x + y - 6= 0, therefore:

$\implies \dfrac{4+a}{2}+ \dfrac{3+b}{2}-6=0\\\implies 4+a+3+b-12=0\\\implies a+b-5=0\\\implies a+b=5$

Slope of AR X Slope of PQ = -1

$-1 \times \dfrac{b-3}{a-4}=-1\\b-3=a-4\\a-b=-3+4\\a-b=-1$

Solving simultaneously

a+b=5

a-b=-1

2a=4

a=2

b=3

Therefore, the coordinates of point Q is (2,3)