Question

In the following figure, the line passes through the origin and through P=(1,3). Find the equation of a line which passes through P and is perpendicular to the first.

A
y=3x+4
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B
y=13x+4
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C
y=13x+103
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D
y=13x+4
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E
y=13x+103
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Solution

The correct option is E y=−13x+103The line shown in the above figure passes through (0,0) and (1,3).So the slope of the line m=y2−y1x2−x1=3−01−0=31=3Thus the line which passes through P(1,3) and perpendicular to the first have a negative reciprocal slope which is −13.So, the equation of the line is⇒y=mx+b⇒3=−13(1)+b⇒3=−13+b⇒b=3+13⇒b=103Put the value to find the equation⇒y=−13x+103

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