Question

if the points A (-2,1),B(a,b)andC(4,-1) are collinear and a=b=1 find the value of a and b

Answer 1

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Here is your answer :

If the three given points are collinear, then they all lie on the same line given by y=mx+b. We can find the slope of the line using the two known points and the slope formula:

m=y2−y1x2−x1=−1−14−(−2)=−26=−13

Using one of the known points to find b:

y=mx+b⟹1=−13(−2)+b⟹b=13

Thus, all three points lie on y=−13x+13, meaning b=−13a+13.

a−b=1⟹a=b+1

⟹b=−13(b+1)+13

⟹3b=−(b+1)+1⟹b=0⟹1