The midpoint of PQ is M=2,−1 One endpoint is
P=7,6. Find the coordinates of the other endpoint, Q.
let the other endpoint be (a,b)
recall how to find the midpoint:
for the x-coordinate, add up the x's of the endpoints , then divide by 2
for the y-coordinate, add up the y's of the endpoints , then divide by 2
so for the x of the endpoint:
(a+7)/2 = 2
a+7 = 4
a = -3
find b in the same way.
check if your answer is reasonable by making a sketch
Well, it seems like someone played a prank on you and hid the coordinates of point Q. Maybe they're playing hide and seek! But don't worry, I'll help you find Q.
Let's use a little mathematical humor to solve this. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
So, we have:
(x-coordinate of P + x-coordinate of Q) / 2 = x-coordinate of M
(y-coordinate of P + y-coordinate of Q) / 2 = y-coordinate of M
Plugging in the given values, we get:
(7 + x-coordinate of Q) / 2 = 2
(6 + y-coordinate of Q) / 2 = -1
Now, let's solve for the missing coordinates:
(7 + x-coordinate of Q) = 2 * 2
(6 + y-coordinate of Q) = 2 * (-1)
7 + x-coordinate of Q = 4
6 + y-coordinate of Q = -2
Solving these equations, we find:
x-coordinate of Q = 4 - 7 = -3
y-coordinate of Q = -2 - 6 = -8
So, the coordinates of point Q are (-3, -8). I hope you catch that sneaky Q hiding somewhere!
To find the coordinates of the other endpoint, Q, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint (M) between two endpoints, P(x1, y1) and Q(x2, y2), is given by:
M = ((x1 + x2)/2, (y1 + y2)/2)
Given that M = (2, -1) and P = (7, 6), we can substitute the known values into the formula:
2 = (7 + x2)/2
-1 = (6 + y2)/2
First, let's solve for x2:
2 = (7 + x2)/2
Multiply both sides of the equation by 2:
4 = 7 + x2
Subtract 7 from both sides of the equation:
4 - 7 = x2
-3 = x2
So, the x-coordinate of point Q is -3.
Now, let's solve for y2:
-1 = (6 + y2)/2
Multiply both sides of the equation by 2:
-2 = 6 + y2
Subtract 6 from both sides of the equation:
-2 - 6 = y2
-8 = y2
So, the y-coordinate of point Q is -8.
Therefore, the coordinates of the other endpoint, Q, are (-3, -8).
To find the coordinates of the other endpoint, Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, M, is the average of the coordinates of the endpoints, P and Q.
Let's denote the coordinates of Q as (x, y). Given that the midpoint, M, is (2, -1), and one endpoint, P, is (7, 6), we can use the midpoint formula to write the following equation:
((7 + x) / 2, (6 + y) / 2) = (2, -1)
To solve for x and y, we can set up the following equations:
(7 + x) / 2 = 2 --> 7 + x = 4 --> x = 4 - 7 --> x = -3
(6 + y) / 2 = -1 --> 6 + y = -2 --> y = -2 - 6 --> y = -8
Therefore, the coordinates of the other endpoint, Q, are (-3, -8).