Question

Using determinants, show that the following points are collinear.
(i) A (3, 7), B (4, -3), C (5, -13)
(ii) P (3, 1), Q (4, 2), C (5, 3)

Answer 1

since slopes of collinear pts are always equal
i)prove that the slope of AB =Slope of BC
ii) prove that the slope of PQ =Slope of QR

Answer 2

Answer:

Step-by-step explanation:

Using determinants, show that the following points are collinear.  

(i) A (3, 7), B (4, -3), C (5, -13)  

(ii) P (3, 1), Q (4, 2), C (5, 3)

These points to be colinear . area enclosed by these points would be zero

hence

(x₁(y₂ - y₃) + x₂(y₃-y₁) + x₃(y₁ - y₂) = 0

A =  x₁ = 3   y₁= 7

B =  x₂ = 4   y₂= -3

C =  x₃ = 5    y₃ = -13

3(-3 -(-13) + 4(-13 -7) + 5(7 -(-3)

= 3*10 + 4(-20) + 5(10)

= 30 -80 + 50

= 0

Hence points are colinear

(x₁(y₂ - y₃) + x₂(y₃-y₁) + x₃(y₁ - y₂) = 0

P =  x₁ = 3   y₁= 1

Q =  x₂ = 4   y₂= 2

R =  x₃ = 5    y₃ = 3

3(2 -3) + 4(3 -1) + 5(1 -2)

= -3 + 8 -5

= -8 + 8

= 0

Hence points are colinear