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3 years ago

14

Mrs .velazco gave her students four options to choose from for the class project

1 answer:

Over [174]3 years ago

3 0

Answer:

Step-by-step explanation:

what are the options

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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><u>Solution:</u></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

<em><u>The slope "m" of the line is given as:</u></em>

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

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)

<em><u>The midpoint formula for given two points is given as:</u></em>

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

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

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

<em><u>The point slope form is given as:</u></em>

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

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

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

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

Find area of 12 inches by 5 inches

tigry1 [53]

Answer:

60 inches

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

Find the value of x........

raketka [301]

Answer:

x=23

Step-by-step explanation:

Hello There!

Remember the exterior angle of a triangle is equal to the opposite interior angles of a triangle

so

137-x=2x+3x-1

now we can solve for x

step 1 combine like terms

2x+3x=5x

now we have

137-x=5x-1

step 2 add 1 to each side

-1+1 cancels out

137+1=138

138-x=5x

step 2 add x to each side

-x+x cancels out

5x+x=6x

now we have

138=6x

step 3 divide each side by 6

6x/6=x

138/6=23

we´re left with x=23

7 0

3 years ago

"Mia jogs 3 kilometers in 20 minutes. There are about 0.6 miles in a kilometer. What is Mia’s approximate speed in miles per min

gladu [14]

Answer:

The correct answer is B: 0.09 miles per minute.

5 0

3 years ago

List the first six common multiples of 6 and 9.

Zepler [3.9K]

6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108

9,18,27,36,45,54,63,72,81,90,99,108

So the first 6 common multiples of 6 and 9 are:

Answer: 18, 36, 54, 72, 90, 108

Hope this Helps!!

8 0

4 years ago