TThe mid-point of a line segment is M(- 3, 2) . One end-point of the segment is P(1,-3). Find the coordinates of the other end point.
If the other endpoint is Q, then we have
Q-M = M-P
Q = 2M-P = 2(-3,2)-(1,-3) = (-6,4)-(1,-3) = (-7,7)
sorry
Q-PQ=2M-P=2(-3;2)-(-6;4)-(1;3)=(77)
Well, let's put on our thinking clown shoes and solve this! We can use the midpoint formula to find the coordinates of the other end-point.
The midpoint formula goes like this: (x₁ + x₂)/2, (y₁ + y₂)/2
We know the midpoint is M(-3, 2) and one end-point is P(1,-3). So let's substitute the values into the formula:
(-3 + x₂)/2 = -3 and (2 + y₂)/2 = -3
Now, let's do some silly math here:
-3 + x₂ = -6 and 2 + y₂ = -6
By adding 3 to both sides of the first equation and subtracting 2 from both sides of the second equation, we get:
x₂ = -3 and y₂ = -8
So, the coordinates of the other end-point are (-3, -8). Ta-da! Clown math strikes again!
To find the coordinates of the other end point, we need to use the mid-point formula. The formula states that the mid-point of a line segment is the average of the coordinates of its end points.
Let's denote the coordinates of the other end point as (x, y).
According to the mid-point formula:
Mid-point (M) = [(x1 + x2) / 2, (y1 + y2) / 2]
Given:
Mid-point (M) = (-3, 2)
One end-point P(1, -3)
Using the formula, we can set up the following equation:
(-3, 2) = [(1 + x) / 2, (-3 + y) / 2]
Now, let's solve the equation for x and y.
First, solve for x:
-3 = (1 + x) / 2
Multiply both sides by 2 to eliminate the fraction:
-6 = 1 + x
Subtract 1 from both sides:
-7 = x
Now, solve for y:
2 = (-3 + y) / 2
Multiply both sides by 2 to eliminate the fraction:
4 = -3 + y
Add 3 to both sides:
7 = y
Therefore, the coordinates of the other end point are (-7, 7).