if the points(-8,4), (-2,4) and (5,a) are collinear points, find the value of a.
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Answer:
let a = ( -8,4 )
let b= ( -2,4 )
let c= ( 5,a )
Distance between a and b
√ ( x2 - x1 ) ^2 + ( y2 - y1 ) ^2
{ distance formula}
√ ( -2 - ( -8 ) ) ^2 + ( 4 - 4 ) ^2
√ ( -2 + 8 ) ^2 + ( 0 ) ^2
√ ( 6 ) ^2 + 0
√ 36
6
:. distance between a and b = 6
they are collinear points, then
AB = BC = AC = 6
Now,
Distance between b and c
√ ( x2 - x1 )^2 + ( y2 - y1 ) ^2
6 = √ ( 5 + 2 ) ^2 + ( a - 4 ) ^2
6 = √ ( 7 ) ^2 + ( a - 4 )^2
6 = √ 49 + ( a - 4 ) × ( a - 4 )
6 = 7 ( a - 4 )
6 = 7a - 28
6 + 28 = 7a
34 = 7a
34 ÷ 7 = a
4.85 = a
a = 4.85
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