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Question

Find the point of intersection of a line passing through (5,3) & (3,5) by a line xy=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 xy=2

Equation of line given the slope m is
yy1=m(xx1)

Slope is given by, m=y2y1x2x1=5335=1

Equation of AB, y3=1(x5)x+y=8

By solving we can find the point of intersection (or common point)

x+y=8xy=2–––––––––2x=10x=5 5+y=8y=3

The point is (5,3)

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