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Question: If the points (–2,–5), (2,–2), (8,a) are collinear, then the value of a is....

If the points (–2,–5), (2,–2), (8,a) are collinear, then the value of a is.

A

52- \frac{5}{2}

B

52\frac{5}{2}

C

32\frac{3}{2}

D

12\frac{1}{2}

Answer

52\frac{5}{2}

Explanation

Solution

Let A be (– 2, – 5), B (2, –2) and C is (8, a), we know that, three points are collinear if slope of AB = slope of BC 2+52+2=a+282a=52\Rightarrow \frac { - 2 + 5 } { 2 + 2 } = \frac { a + 2 } { 8 - 2 } \Rightarrow a = \frac { 5 } { 2 } .