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puteri [66]
2 years ago
15

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

Mathematics
2 answers:
masya89 [10]2 years ago
5 0

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.

KiRa [710]2 years ago
4 0

Answer:

A

Step-by-step explanation:

Edge 2020

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