if the points (-8,4),(-2,4) and (5,a) are collinear points .find a
by distance formula
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Answered by
1
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Since the given points are collinear, they do not form a
triangle, which means area of the triangle is Zero.
Area of a triangle with vertices (x
1
,y
1
) ; (x
2
,y
2
) and (x
3
,y
3
) is
∣
∣
∣
∣
2
x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)
∣
∣
∣
∣
Hence, substituting the points (x
1
,y
1
)=(8,1) ; (x
2
,y
2
)=(k,−4) and (x
3
,y
3
)=(2,−5)
the area formula, we get
∣
∣
∣
∣
2
8(−4+5)+k(−5−1)+2(1+4)
∣
∣
∣
∣
=0
=>8−6k+10=0
=>6k=18
=>k=3.
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