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The midpoint M of CD has coordinates (5, 4). Point D has coordinates (10, 2). Find the coordinates of point C.

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Answer: coordinates of point C are (0, 6)

Explanation:

To find the coordinates of point C, you can use the midpoint formula in reverse. The midpoint formula is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

You already have the midpoint, which is (5, 4), and the coordinates of point D, which is (10, 2). Let's call the coordinates of point C (xC, yC).

Plugging the values into the formula:

Midpoint = ((xC + 10) / 2, (yC + 2) / 2)

(5, 4) = ((xC + 10) / 2, (yC + 2) / 2)

Now, you can solve for xC and yC. Start with the x-coordinate:

5 = (xC + 10) / 2

Multiply both sides by 2 to isolate xC:

10 = xC + 10

Now, subtract 10 from both sides to find xC:

xC = 10 - 10

xC = 0

Now, find the y-coordinate using the same approach:

4 = (yC + 2) / 2

Multiply both sides by 2 to isolate yC:

8 = yC + 2

Subtract 2 from both sides to find yC:

yC = 8 - 2

yC = 6

So, the coordinates of point C are (0, 6).

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