Question

The given line segment has a midpoint at (3,1)

Answer 1

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

We have been given an image of a line segment and we are asked to find the equation of perpendicular bisector of our given line segment in slope-intercept form.

Since we know that the slope of perpendicular line to a given line is negative reciprocal of the slope of the given line.

Let us find the slope of our given line using slope formula.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$, where,

$y_2-y_1$ = Difference between two y-coordinates,

$x_2-x_1$ = Difference between two x-coordinates of same y-coordinates.

Upon substituting the coordinates of points (2,4) and (4,-2) in slope formula we will get,

$\text{Slope}=\frac{-2-4}{4-2}$

$\text{Slope}=\frac{-6}{2}$

$\text{Slope}=-3$

Now we will find negative reciprocal of $-3$ to get the slope of perpendicular line.

$\text{Negative reciprocal of }-3=-(-\frac{1}{3})=\frac{1}{3}$

Since point (3,1) lies on the perpendicular line, so we will substitute coordinates of point (3,1) in slope-intercept form of equation $(y=mx+b)$.

$1=\frac{1}{3}\times 3+b$

$1=1+b$

$1-1=1-1+b$

$b=0$

Therefore, the equation of perpendicular line will be $y=\frac{1}{3}x+0=\frac{1}{3}x$ and option A is the correct choice.

Answer 2

Answer:

A

Step-by-step explanation:

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