Question

Plot the following point and verify if it is collinear.

P(−2, −1), Q(2, 1) and R(8, 4)

Answer 1

Area of Triangle Method:

Area = `1/2 |x_1(y_2 − y3) + x_2(y_3 − y_1) + x_3(y_1 − y_2)|`   ... [use the area of triangle method]

Area = `1/2 |−2 (1 − 4) + 2(4 − (− 1)) + 8 ((− 1) − 1|`

Area = `1/2|− 2 (−3) + 2(5) + 8(−2) |`

Area = `1/2 |6 + 10 − 16|`

Area = `1/2 (0)`

Area = 0

Slope Method:

Slop of PQ:

`m_(PQ) = (1 − (− 1))/(2 − (− 2))`

= `2/4`

= `1/2`

Slop of QR

= `m_(QR)​`

= `(4 − 1)/(8 − 2)`

= `3/6`

= `1/2`

Since `m_PQ = m_(QR)`

= `1/2`

Points P(−2, −1), Q(2, 1) and R(8, 4) are collinear.