Question

If one endpoint of AD is A(-3,-8) and the midpoint of AD is M(3,-4) what is the other endpoint D?

Answer 1

to help you answer your question ill ask you a question. When you draw out the points how many points is it from A (-3,-8) to Point M(3,-4)

Answer 2

you'll continue that many points in the same direction to get the Endpoint D

Answer 3

Is there a equation i can use or do i just map it out?

Answer 4

mapping it out shouldnt be tough

Answer 5

just use a piece of graph paper (:

Answer 6

you can use this if yu dont have graph paper http://www.garrettbartley.com/graphpaper.html

Answer 7

i got you rise 4 and slide 6:)

Answer 8

thats not a option on my choices tho its..
A 3.-4
B-7,11
C 7,-6
D 9,0

Answer 9

this is so confusing xD HAHA

Answer 10

you need to put the actual coordinates you got at the D Endpoint i think

Answer 11

Huhhh?

Answer 12

you know the midpoint formula?

Answer 13

\(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({\color{red}{ -3}}\quad ,&{\color{blue}{ -8}})\quad
% (c,d)
D&({\color{red}{ \square }}\quad ,&{\color{blue}{ \square }})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)=M\)


follow that? if you dunno the midpoint formula... you may want to refresh on that one first

Answer 14

use this https://www.sophia.org/tutorials/applying-the-midpoint-formula-with-one-endpoint--11

Answer 15

we now what A coordinates are
we dunno what D coordinates

we also know that the coordinates for M are

so we can use that and say that \(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({\color{red}{ -3}}\quad ,&{\color{blue}{ -8}})\quad
% (c,d)
D&({\color{red}{ \square }}\quad ,&{\color{blue}{ \square }})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{\color{red}{ \square }} + {\color{red}{ (-3)}}}{2}\quad ,\quad \cfrac{{\color{blue}{ \square }} + {\color{blue}{ (-8)}}}{2} \right)=M
\\ \quad \\
M=(3,-4)\qquad thus
\\ \quad \\
\left(\cfrac{{\color{red}{ \square }} + {\color{red}{ (-3)}}}{2}\quad ,\quad \cfrac{{\color{blue}{ \square }} + {\color{blue}{ (-8)}}}{2} \right)=M
\\ \quad \\

\left(\cfrac{{\color{red}{ \square }} + {\color{red}{ (-3)}}}{2}\quad ,\quad \cfrac{{\color{blue}{ \square }} + {\color{blue}{ (-8)}}}{2} \right)=(3,-4)\implies
\begin{cases}
\cfrac{{\color{red}{ \square }} + {\color{red}{ (-3)}}}{2}=3
\\ \quad \\
\cfrac{{\color{blue}{ \square }} + {\color{blue}{ (-8)}}}{2}=-4
\end{cases}\)


so just solve for the ones you don't have

Answer 16

and recall that D is \(\bf ({\color{red}{ \square }}\quad ,{\color{blue}{ \square }})\)

so.. whatever those variables are, is D coordinates