Question

A(-2,-5),B(2,3) and C (8,a) are collinear.Find the value of a.

Answer 1

Step-by-step explanation:

above is answer of this question

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Answer 2

Given : The three collinear points are, A(-2,-5),B(2,3) and C (8,a)

To find : The value of a

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of a)

If three points are collinear, then we will not form any triangle. In other words, the area of the triangle made by three collinear points will be 0.

If three points are :

• (x1,y1)
• (x2,y2)
• (x3,y3)

Then the area of the triangle made by these points will be :

= ½ × [x1 (y2-y3) + x2 (y3-y1) + x3 (y1-y2)]

Similarly, the area of the triangle made by the given three points will be :

= ½ × [-2 (3-a) + 2 (a+5) + 8 (-5-3)]

= ½ (-6+2a+2a+10-64)

= ½ (4a-60)

= (2a-30) sq. units

As the three points are collinear :

2a-30 = 0

2a = 30

a = 30/2

a = 15

Hence, the value of a is 15