Question

If the points (-8,4), (-2,4) and (5,a) are
collinear points, find the value of a.

​

Answer 1

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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Answer 2

Answer:

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Step-by-step explanation:

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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