Question

Find the relation between x and y if points (2, 1), (x, y) and (7, 5) are collinear.​

Answer 1

Answer-

Given,

x1=2, y1=1

x2=x, y2=y

x3=7, y3=5

Step-by-step explanation:

Area of triangle =1/2[x1(y2−y3)+x2(y3−y1)+x3(y1−y3)]

=1/2[2(y−5)+x(5−1)−7(1−y)]

given that the points (2,1), (x,y) and (7,5), then area of triangle must be zero.

∴1/2[2(y−5)+x(5−1)−7(1−y)]=0

⇒1/2[2y−10+5x−x+7−7y]=0

⇒1/2(−5y+4x−3)=0

⇒4x−5y−3=0

Then, relation between x and y is 4x−5y−3=0

Answer 2

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