Question

Plot A(3, 0) and B(8, 5). If points C(2, p) and D(q, 1) lie on the line AB, find the values of p and q.

Answer 1

Given:

A(3, 0), B(8, 5)

C(2, p) and D(q, 1) lie on line AB.

Need to find p and q

Step 1: Find slope of AB

`"Slope"_(AB) ​= (5 − 0)/(8 − 3)`

= `5/5`

= 1

Equation of line AB (using point A(3,0)):

y − 0 = 1(x − 3)

y = x − 3

Step 2: Find p for C(2, p)

Since C lies on AB:

y = x − 3

Put x = 2

p = 2 − 3 

p = −1

Step 3: Find q for D(q, 1)

y = x − 3

Put y =1

1 = q − 3

q = 4