Mathematics, 29.10.2020 22:40 isaacbrown7one

Find the midpoint of PQ with endpoints P(-5, -5) and Q (3, 3). Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is the perpendicular bisector.

Answers: 1

Show answers

Answers

Answer from: dontrailgrant98

The equation of the line that passes through the midpoint and is perpendicular to PQ is $\rm \bold{ y = -x -2}$

Coordinates of P are (-5.-5)

Coordinates of Q are ( 3,3)

The midpoint of the PQ can be found out by the formula given in equation (1)

$\rm (x , y) = ((x_1 +x_2)/2, (y_1+y_2)/2 ).........(1) \\\\Where\; (x_1,y_1) \; and \; (x_2,y_2) are\; the\; coordinates\; of\; two\; given \; points \; that \; make \; the \; line$

The midpoint of line joining P and Q we can find out the by putting coordinates in equation (1)

Let O be the mid point of PQ

We can write that the coordinates of O

$\rm ((-5 +3)/2 , (-5 + 3) /2 ) = (-1,-1)$

The slope of line passing through two points

$\rm (x_1, y_1)\; and \; (x_2,y_2) \\\\m = \dfrac{y_2 -y_1}{x_2-x_1}$

Slope of line passing through P and Q is given

$\rm \\\\m = \dfrac{y_2 -y_1}{x_2-x_1} = \dfrac{3-(-5)}{3-(-5)} = \dfrac{8}{8} = 1$

Let the slope of line that is perpendicular is M

hence the slope M can be found out in the following way

$\rm m \times M = -1 \\1\times M = -1 \\M = - 1$

Let the equation of line passing through point O

(-1,-1) with slope M is given as formulated in equation (2)

$\rm y = Mx +c......(2)$

Point O (-1,-1) will satisfy the equation of line

$\rm -1 = -M + c \\-1 = 1 + c\\c = -2$

On putting the values of c and M in equation (2) we get equation of line

$\rm \bold{ y = -x -2}$

So, The equation of the line that passes through the midpoint and is perpendicular to PQ is $\rm \bold{ y = -x -2}$

For more information please refer to the link given below

link

Answer from: bryan9892

y = -x-2

Step-by-step explanation:

The formula for calculating the midpoint is expressed as:

M(X, Y) = [(x2+x1)/2, (y2+y1)/2]

Given the coordinates P(-5, -5) and Q (3, 3)

Midpoint = [-5+3/2, -5+3/2]

Midpoint = (-2/2, -2/2)

Midpoint = (-1, -1)

Next is to find an equation of the line that passes through the midpoint and is perpendicular to PQ.

The standard form of equation of a line is y = mx+c

Get the slope m:

m = y2-y1/x2-x1

m = 3-(-5)/3-(-5)

m = 8/8

m = 1

For two lines to be perpendicular, the poduct of their slope must be -1

mM = -1

M(1) = -1

M = -1/1

M = -1

To get the slope, substitute the midpoint (-1,-1) and the slope m = -1 into the equation y = mx+c

-1 = -1(-1)+c

-1 = 1+c

c = -1-1

c = -2

Substitute M =-1 and c = -2 into the equation to get the equation of the required line;

y = Mx+c

y = (-1)x-2

y = x-2

Hence the required equation is y = -x-2

Answer from: Quest

based on context clues you gave i'm assuming the answer would be c.

Pls on time limit : 3 what does this map portray? a. the direction of wind patterns in italy. c. t

Answer from: Quest

answer: it is 1: 47 pm

Another question on Mathematics

Mathematics, 21.06.2019 13:10

In the surface area formula for cylinders which expressionrepresents the lateral area

Answers: 1

Answer

Mathematics, 21.06.2019 15:30

The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −5 0 −1 1 3 g(x) g(x) = 2x − 7 part a: write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) part b: which function has a greater y-intercept? justify your answer. (4 points)

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

What percent of the circle below is shaded?

Answers: 1

Answer

Mathematics, 22.06.2019 02:00

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?

Answers: 1

Answer

You know the right answer?

Find the midpoint of PQ with endpoints P(-5, -5) and Q (3, 3). Then write an equation of the line th...

Questions

Mathematics, 19.01.2021 18:50

Angela puts $520 in an account that earns 6% per year. What interest will she get at the end of 1 year?...