Question

The midpoint of GH is M(6,-7). One endpoint is H(4,-4). Find the coordinates of endpoint G.

a) 8,−108,−10
b) 2,−142,−14
c) 8,−148,−14
d) 2,−102,−10

Answer 1

The coordinates of endpoint G, given the midpoint M(6,-7) and one endpoint H(4,-4), are (8, -10). To find this, we use the midpoint formula and solve for the unknown coordinates of G.

Step-by-step explanation:

To find the coordinates of endpoint G when you are given the midpoint M and one endpoint H, you can use the midpoint formula which states that the midpoint M is the average of the x-coordinates and the y-coordinates of the endpoints G and H. In mathematical terms, this is written as M = ((xG + xH)/2, (yG + yH)/2).

Given the midpoint M(6,-7) and one endpoint H(4,-4), we can set up the following equations to find the coordinates of the other endpoint G:

• 6 = (xG + 4)/2
• -7 = (yG - 4)/2

To find xG, we solve 6 = (xG + 4)/2:

12 = xG + 4

xG = 12 - 4 = 8

Similarly, to find yG, we solve -7 = (yG - 4)/2:

-14 = yG - 4

yG = -14 + 4 = -10

Therefore, the coordinates of G are (8, -10).