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write an equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

dimaraw [331]

The equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is $y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

<h3>Solution:</h3>

Given that we have to write equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

Let us first find the slope of given line AB

The slope "m" of the line is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here the given points are A(-2,2) and B(5,4)

$\text {Here } x_{1}=-2 ; y_{1}=2 ; x_{2}=5 ; y_{2}=4$

$m=\frac{4-2}{5-(-2)}=\frac{2}{7}$

Thus the slope of line with given points is $\frac{2}{7}$

We know that product of slopes of given line and slope of line perpendicular to given line is always -1

$\begin{array}{l}{\text {slope of given line } \times \text { slope of perpendicular bisector }=-1} \\\\ {\frac{2}{7} \times \text { slope of perpendicular bisector }=-1} \\ \\{\text {slope of perpendicular bisector }=\frac{-7}{2}}\end{array}$

The perpendicular bisector will run through the midpoint of the given points

So let us find the midpoint of A(-2,2) and B(5,4)

The midpoint formula for given two points is given as:

$\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { midpoint } \mathrm{m}(x, y) \text { is given as }$

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Substituting the given points A(-2,2) and B(5,4)

$m(x, y)=\left(\frac{-2+5}{2}, \frac{2+4}{2}\right)=\left(\frac{3}{2}, 3\right)$

Now let us find the equation of perpendicular bisector in point slope form

The perpendicular bisector passes through points (3/2, 3) and slope -7/2

The point slope form is given as:

$y - y_1 = m(x - x_1)$

$\text { Substitute } \mathrm{m}=\frac{-7}{2} \text { and }\left(x_{1}, y_{1}\right)=\left(\frac{3}{2}, 3\right)$

$y - 3 = \frac{-7}{2}(x - \frac{3}{2})\\\\y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

Thus the equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is found out

7 0

4 years ago

Question 4 of 6, Step 3 of 4

Goshia [24]

Well let’s see u don’t know the answer your question but I’m sure someone would love to help you

6 0

4 years ago

4 QUESTIONS 20 POINTS

storchak [24]

Coresponding is
1to5
4to8
3to7
2to6
pick 2 pairs (there are 4 pairs)

alternate interior angles are
4and5
3and6

angle7=angle6=angle2=angle3=106 degrees

angle7+angle8=180
106+angle8=180
angle8=74

1to5
4to8
3to7
2to6
pick 2 pairs (there are 4 pairs)

alternate interior angles are
4and5
3and6

angle7=106 degrees

angle8=74

5 0

3 years ago

PICTURE ABOVE find perimeter in inches PLEASE HELP !!!

Vsevolod [243]

Answer:

C. 52

Step-by-step explanation:

First, find the base of the triangle. You can do this by looking at the top of the figure. 14 inches is the width of the rectangle, and 20 inches is the width of the rectangle and the base of the triangle. You can find the base of the triangle by subtracting.

$20-14=6$

The base of the triangle is 6. The height of the triangle is equal to the height of the rectangle, 8. Now you need to find the hypotenuse of the triangle using the Pythagorean theorem:

$a^2+b^2=c^2$