Question

if the points (a 0) (0 b) and (7 -5) are collinear prove that 2/b+3/a=1

Answer 1

Answer:

Given : Points (- 2, 5), (0, 1) and (2, - 3)  

To prove : Given points are collinear.

 

Solution :  

Let A(- 2, 5), B(0, 1) and C(2, - 3)  are the vertices  

 

By using distance formula : √(x2 - x1)² + (y2 - y1)²

Vertices : A(- 2, 5), B(0, 1)  

Length of side AB = √(0 + 2)² + (1 - 5)²

AB = √2² + (4)²

AB = √4 + 16

AB = √20

AB= √(5 × 4)

AB = 2√5 units

Vertices :  B(0, 1) and C(2, - 3)

Length of side BC = √( 2 - 0)² + (- 3 - 1)²

BC = √(2)² + (-4)²

BC = √4 + 16

BC = √20  

BC = √(5 × 4)

BC = 2√5 units

 

Vertices :   A(- 2, 5), C(2, - 3)

Length of side AC = √(2 + 2)² + (- 3 - 5)²

AC = √(4)² + (-8)²

AC = √16 + 64

AC = √80 units

AC = √(16 × 5)

AC =  4√5  units

Since the length of AB + BC = AC  ,  2√5 + 2√5  =  4√5

Hence the points are collinear.

Step-by-step explanation: