The midpoint of BC is M(-10,-16). One endpoint is B(-1,8). What are the coordinates of C?
The midpoint of BC is M(-10,-16)
B(-1,8) C = ?
xm = 1/2(x1 + x2), ym = 1/2(y1 + y2)
-10 = 1/2(-1 + x2)
-20 = -1 + x2
-19 = x2
-16 = 1/2(8 + y2)
-32 = 8 + y2
-40 = y2
C(-19, -40)
check my math
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Well, C is certainly not H(-69,420) if that's what you were hoping for. But let's figure out the coordinates of C anyways, shall we?
To find the coordinates of C, we need to use the midpoint formula, which states that the coordinates of the midpoint (M) are equal to the average of the coordinates of the endpoints (B and C). You know that M is (-10,-16) and B is (-1,8), so let's do some math!
(-10,-16) = ((-1 + x)/2, (8 + y)/2)
Now we just need to solve for x and y. Let's do this together, shall we? *cracks knuckles*
For the x-coordinate:
-10 = (-1 + x)/2
-20 = -1 + x
x = -19
For the y-coordinate:
-16 = (8 + y)/2
-32 = 8 + y
y = -40
So the coordinates of point C are (-19, -40). Voila!
To find the coordinates of point C, we need to use the concept of the midpoint formula.
The midpoint formula states that the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) can be calculated using the following formulas:
Midpoint X-coordinate (Mx) = (x₁ + x₂) / 2
Midpoint Y-coordinate (My) = (y₁ + y₂) / 2
We are given:
Endpoint B: B(-1, 8)
Midpoint M: M(-10, -16)
Using the midpoint formula, we can substitute the given values into the formula to find the missing endpoint C.
Midpoint X-coordinate (Mx) = (x₁ + x₂) / 2
-10 = (-1 + x₂) / 2
Solving for x₂:
Multiply both sides by 2:
-20 = -1 + x₂
Add 1 to both sides:
-19 = x₂
So, the x-coordinate of point C is -19.
Midpoint Y-coordinate (My) = (y₁ + y₂) / 2
-16 = (8 + y₂) / 2
Solving for y₂:
Multiply both sides by 2:
-32 = 8 + y₂
Subtract 8 from both sides:
-40 = y₂
So, the y-coordinate of point C is -40.
Therefore, the coordinates of point C are (-19, -40).