Question

# Find the point of intersection of a line passing through (5,3) & (3,5) by a line x−y=2.

A
(5,5)
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B
(3,3)
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C
(5,3)
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D
(3,5)
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Solution

## The correct option is C (5,3)Given, Consider A(5,3) & B(3,5) & line x−y=2 Equation of line given the slope m is y−y1=m(x−x1) Slope is given by, m=y2−y1x2−x1=5−33−5=−1 Equation of AB, y−3=−1(x−5)⇒x+y=8 By solving we can find the point of intersection (or common point) x+y=8x−y=2–––––––––––2x=10⇒x=5 5+y=8⇒y=3 The point is (5,3)

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