Question

Points (5,2), (1,0) and (a,5) lie on the same straight line. Then the value of a is a) 15 b) 13 c)11 d)9​

Answer 1

C

Explanation:

Since the points lie on the same line then the slope between consecutive points will be the same.

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (5, 2) and (x₂, y₂ ) = (1, 0)

m =
`(0-2)/(1-5)` =
`(-2)/(-4)` =
`(1)/(2)`

Calculate the slope again and equate to
`(1)/(2)`

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (a, 5)

m =
`(5-0)/(a-1)` =
`(1)/(2)` , so

`(5)/(a-1)` =
`(1)/(2)` ( cross- multiply )

a - 1 = 10 ( add 1 to both sides )

a = 11

Answer 2

Hello,

the line passing through (5,2) and (1,0) has for equation:

y-0=(x-1)*(-2)/(-4) or y=x/2-0.5

if y= 5 then 5=x/2-0.5 ==> 5.5=x/2 ==> x=11

Answer C