M(1, 7) is the midpoint of PQ¯¯¯¯¯ . The coordinates of point P are (−8, 3) .
What are the coordinates of point Q?
Q is as far from M , as M is from P
9 in the x-direction ... 1 - -8
... Qx = Mx + 9
4 in the y-direction ... 7 - 3
... Qy = My + 4
so the answer is 9,4?
"so the answer is 9,4?" ... no
Q = [(Mx + 9),(My + 4)]
To find the coordinates of point Q, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) is given by:
Midpoint = [(x1 + x2)/2 , (y1 + y2)/2]
In this case, we know the midpoint M(1, 7) and one of the points P(-8, 3). Let's substitute the values into the formula to find the coordinates of point Q.
We have:
Midpoint = [(x1 + x2)/2 , (y1 + y2)/2]
M(1, 7) = [(-8 + x2)/2 , (3 + y2)/2]
Since M is the midpoint of PQ, we can equate the coordinates of M with the coordinates of Q and solve for x2 and y2:
1 = (-8 + x2)/2 , 7 = (3 + y2)/2
First, let's simplify the equations:
1 = (-8 + x2)/2 => 2 = -8 + x2 => x2 = 10
7 = (3 + y2)/2 => 14 = 3 + y2 => y2 = 11
Therefore, the coordinates of point Q are (10, 11).