Point M is the midpoint of line PQ. The coordinates of P and M are:
P: 5, (-2)
M: 11, (-10)
Given this info, what are the coordinates of Q?
I'm having trouble understanding what I'm supposed to do with this problem. Anyone willing to explain it to me would be very appreciated.
Q is just as far from M as M is from P. That is,
Q-M = M-P
Q = M + (M-P) = (11,-10) + (6,-8) = (17,-18)
Thank you oobleck.
P(5, -2), M(11, -10), Q(x, y).
x-5 = 2(11-5)
X = 17.
y+2 = 2(-10+2)
Y = -18.
To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two points P(x₁, y₁) and Q(x₂, y₂) are:
M͟x = (x₁ + x₂) / 2
M͟y = (y₁ + y₂) / 2
In this case, we already know the coordinates of point M (11, -10) and point P (5, -2), and we need to find the coordinates of point Q.
Let's substitute the known values into the formula:
M͟x = (5 + x₂) / 2
M͟y = (-2 + y₂) / 2
Since M is the midpoint between P and Q, we can say that M has the same coordinates as the midpoint:
11 = (5 + x₂) / 2
-10 = (-2 + y₂) / 2
Now, we can solve these equations to find the coordinates of Q.
For the x-coordinate:
11 = (5 + x₂) / 2
Multiply both sides of the equation by 2 to remove the fraction:
22 = 5 + x₂
Subtract 5 from both sides of the equation:
17 = x₂
So, the x-coordinate of point Q is 17.
Next, let's find the y-coordinate:
-10 = (-2 + y₂) / 2
Multiply both sides of the equation by 2 to remove the fraction:
-20 = -2 + y₂
Add 2 to both sides of the equation:
-18 = y₂
So, the y-coordinate of point Q is -18.
Therefore, the coordinates of point Q are (17, -18).