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aalyn [17]
3 years ago
14

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unkno

wn endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)
Midpoint (-15,2) endpoint (-12,11)
What is the other endpoint?
Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
5 0

Answer:

The other endpoint of the​ segment is (-18,-7).

Step-by-step explanation:

The midpoint of the points (x_1,y_1) and (x_2,y_2) is given by the following formula:

                                          (x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}  )

where (x_m,y_m) = coordinates of the midpoint.

We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:

                                         (-15,2)=(\frac{x_1-12}{2}, \frac{y_1+11}{2}  )

To find x_1 we need to solve this equation:

-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18

and to find y_1 we need to solve this equation:

2= \frac{y_1+11}{2}  \\\\\frac{y_1+11}{2}=2\\\\\frac{2\left(y_1+11\right)}{2}=2\cdot \:2\\\\y_1+11=4\\\\y_1=-7

The other endpoint of the​ segment is (x_1,y_1)=(-18,-7).

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