One endpoint of a line segment has coordinates represented by (x+4,1/2y). The midpoint of the line segment is (3,−2).

How are the coordinates of the other endpoint expressed in terms of x and y?

Answer:

[tex]\displaystyle \left(-x+2, -\frac{1}{2}y-4}\right)[/tex]

Step-by-step explanation:

We are given that one of the endpoints of the line segment is:

[tex]\displaystyle \left( x + 4, \frac{1}{2}y\right)[/tex]

And that the midpoint of the line segment is (3, -2).

And we want to find the other coordinates in terms of x and y.  

We can consider using the midpoint formula:

[tex]\displaystyle M = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]

We are given that the midpoint is (3,-2). Substitute:

[tex]\displaystyle (3, -2) = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]

We can solve for each coordinate independently.

x-coordinate:

We have:

[tex]\displaystyle 3=\frac{x_1+x_2}{2}[/tex]

One of the two endpoints is (x + 4, 1/2y). Hence, we can substitute x + 4 for x₁:

[tex]\displaystyle 3=\frac{(x+4)+x_2}{2}[/tex]

Solve for the second x-coordinate x₂:

[tex]\displaystyle \begin{aligned} 6 & = x+4 + x_2 \\ \\ x_2 + x & = 2 \\ \\ x_2 & = -x +2 \end{aligned}[/tex]

Hence, the x-coordinate of the second point is -x + 2.

y-coordinate:

We have:

[tex]\displaystyle -2=\frac{y_1+y_2}{2}[/tex]

We can substitute 1/2y for y₁. This yields:

[tex]\displaystyle -2=\frac{\dfrac{1}{2}y+y_2}{2}[/tex]

Solve for y₂:

[tex]\displaystyle \begin{aligned} -4 & = \frac{1}{2}y + y_2 \\ \\ y_2 & = -\frac{1}{2}y - 4\end{aligned}[/tex]

In conclusion, the other coordinate expressed in terms of x and y is:

[tex]\displaystyle \left(-x+2, -\frac{1}{2}y-4}\right)[/tex]

Answer:

This is for a different question the answer above is correct because I used it steps. Now the question below is similar and is on the test.

Step-by-step explanation:

Please help !! I am having trouble, I keep getting this question wrong.

What is an equation of the line that passes through the points (0, -2) and (6,6)

I will give you branilest!

When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.


cups of blue paint cups of yellow paint
2 10
1 5
3 15

.

4. What is the constant of proportionality in the table? (choose one)
a. 5
b. 8
c. 9
d. 1

angles 2 and angle 7 are ??? angles​

Three consecutive integers add up to 258. What is the smallest integer?

You are assigned 32 math questions for homework. You complete 87.5% of these before dinner. How many questions do you have left to do after dinner?

In the diagram g|| h, m<1=(4x+36) and m<2=(3x-3)

What is the measure of <3

10times larger than 40

HELP ASAP I have no clue what to do here pls just click the picture and help :(

Please help it’s urgent!!!!!

Find the total surface area of this cuboid,
5 cm
4 cm
6 cm
what is the total surface area

Ceftriaxone 125 mg IM. If I use 1 g/9.6 mL to fill the order, how many mL will I need

Kenya used a debit card to buy a pair of jeans. Which statement is true about her method of payment? Kenya used money directly from her bank account to buy the jeans. Kenya borrowed the money to buy the jeans. Kenya did not have enough money in her bank account to buy the jeans. Kenya will pay for the jeans over time.

10 times as many as 2 hundred is 20 hundreds or 2 thousand

There are 70 fish in the tank. Half of the fish have orange spots and 1/5 of the remaining fish have orange and black spots. How many fish have orange and black spots?

Find the difference: 25.050 - 9.169 =

what is 150 divided by 12

What is the relationship between a and b. ?

Will give brainiest answer and please give an explanation why?

hello please help will give brainliest!

(6*10^3)(2*10^5)
HELP please

A parachutists speed during a free fall reaches 153 miles per hour. What is this speed in feet per second? at this speed, how many feet will the parachutist fall during 15 seconds of free fall? in your computations, use the fact that 1 mile is equal to 5280 feet. do not round your answer

What is (1 x 10(5) + (3 x 10(3) + (7 x 10(2) in standard form?
A. 1,030,700
B. 1,037,000 I. C. 103,700
D. 1,370

8.5 x 103 - 5.3 x 103 -1.0 x 102

The given table values represents a liner equation. What is the slope?

A. 2
B. 3
C. 1
D. 4

What is the slope-intercept equation of the line below?
5
-5
H
O A. y = 2x+1
O B. y=-2x+1
O C. y= 2x-1
O D. y=-2x-1

Systems of equations. Will give brainlest!

a veterinarians office has 2100 animals it sees in one month. of these animals, 1500 of them are dogs. what is the ratio of dogs to all animals, in simplest form?

sin theta= 0.86
sin theta= -0.05
cos theta = 0
0= -2-2tan theta
-3 + 1/4 tan theta = -11/4
4-8cos theta= 0
4= 3tan^2 theta + 3
4sin^2 theta-5 = -4
root 2 tan theta + 2 tan theta = -2 tan theta cos theta + 2 tan theta
3cos theta- 2 cos^2 theta =1
2 root 3 sin^2 - sin^2 theta = 3 sin theta - sin^2 theta


ILL GIVE BRAINLIEST

Alex would like to buy one pack of colored pencils