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Question

If the line passing through (4,3) and (2,k) is perpendicular to y=2x+3, then k=?


A

-1

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B

1

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C

-4

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D

4

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Solution

The correct option is D

4


Explanation for correct option

Step 1: Evaluate the slope of the given points

Given points are (4,3) and (2,k)

Let the slope be m1=y2-y1x2-x1

So, m1=k-32-4=k-3-2

Step 2: Evaluate the slope of the given line

Given equation of the line, y=2x+3

Let the slope-intercept form of line be y=m2x+b

So, m2=2

Step 3: Solve for the given variable

It is given that the points joining together are perpendicular to the equation of the line

So, m1×m2=-1

k-3-2×2=-1k-3=1k=4

Therefore, option (D) is the correct answer.


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