Question

Plot P(−2, 4) and Q(4, 1). If line PQ passes through R(a, 3) and S(2, b), find the values of a and b.

Answer 1

Step 1: Find slope of PQ

Slope PQ,

= `(1 − 4)/(4 − (−2))`

= `(− 3)/6`

= `− 1/2`

So, the equation of line PQ using point-slope form (using P(–2, 4))

y − 4 = −`1/2(x + 2)`

y − 4 = − `1/2 x − 1`

y = − `1/2x + 3`

Step 2: Find a when point R(a, 3) lies on PQ

y = − `1/2x + 3`

Put y = 3

3 = − `1/2a + 3`

0 = `− 1/2a`

a = 0

Step 3: Find b when point S(2, b) lies on PQ

Equation:

y = − `1/2x + 3`     ...[Put x = 2]

b = − 1 + 3

b = 2