Mathematics, 01.06.2021 18:50 AaronMicrosoft15

Find an equation for the perpendicular bisector of the line segment whose endpoints (5, -3) and (-7, -7).
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Answer from: clairajogriggsk

y=-3x-8

Step-by-step explanation:

Hi there!

What we need to know:

Midpoint: $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$ where the endpoints are (x_1,y_1)

and

Linear equations are typically organized in slope-intercept form: y=mx+b

where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 3/4 and -4/3, etc.)

1) Determine the midpoint of the line segment

When two lines bisect each other, they intersect at the middle of each line, or the midpoint.

$(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

Plug in the endpoints (5, -3) and (-7, -7)

$(\frac{5+(-7)}{2} ,\frac{-3+(-7)}{2} )\\(\frac{-2}{2} ,\frac{-10}{2} )\\(-1,-5)$

Therefore, the midpoint of the line segment is (-1,-5).

2) Determine the slope of the line segment

Recall that the slopes of perpendicular lines are negative reciprocals. Doing this will help us determine the slope of the perpendicular bisector.

Slope = $\frac{y_2-y_1}{x_2-x_1}$ where the given points are (x_1,y_1) and (x_2,y_2)

Plug in the endpoints (5, -3) and (-7, -7)

$\frac{-7-(-3)}{-7-5}\\\frac{-7+3}{-7-5}\\\frac{-4}{-12}\\\frac{1}{3}$

Therefore, the slope of the line segment is $\frac{1}{3}$ . The negative reciprocal of $\frac{1}{3}$ is -3, so the slope of the perpendicular is -3. Plug this into y=mx+b :

y=-3x+b

3) Determine the y-intercept of the perpendicular bisector (b)

y=-3x+b

Recall that the midpoint of the line segment is is (-1,-5), and that the perpendicular bisector passes through this point. Plug this point into y=-3x+b and solve for b:

$-5=-3(-1)+b\\-5=3+b$

Subtract 3 from both sides

$-5-3=3+b-3\\-8=b$

Therefore, the y-intercept of the line is -8. Plug this back into y=-3x+b :

y=-3x-8

I hope this helps!

Answer from: Quest

$x=\frac{3}{4}$

step-by-step explanation:

we are given

$-6+2x=6x-9$

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

$-6+2x-2x=6x-9-2x$

$-6=4x-9$

add both sides by 9

$-6+9=4x-9+9$

$3=4x$

divide both sides by 4

we get

$x=\frac{3}{4}$

Answer from: Quest

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

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Find an equation for the perpendicular bisector of the line segment whose endpoints (5, -3) and (-7...

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