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Question

# A straight line passes through the points (2,4) and (5,âˆ’2). Taking 1cm=1 units, mark these points on a graph paper and draw the straight line through these points. If points (m,âˆ’4) and (3,n) lie on the drawn line, find the values of m and n.

A
m=1 and n=2
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B
m=3 and n=2
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C
m=6 and n=2
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D
m=9 and n=2
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Solution

## The correct option is C m=6 and n=2Equation of a straight line passing through(x1,y1) and (x2,y2) is[y−y1=y2−y1x2−x1(x−x1)]here (x1,y1)=(2,4) and (x2,y2)=(5,−2)y−4=−2−45−2(x−2)3y−12=−6x+126x+3y=24(m,−4) and (3,n) lie on the line then,6m−12=246m=36m=618+3m=243m=6n=2Therefore m=6 and n=2

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