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Maksim231197 [3]
3 years ago
6

5. Mis the midpoint of CD. C has coordinates (-1,-1) and

Mathematics
1 answer:
lana66690 [7]3 years ago
7 0

Answer/Step-by-step Explanation:

4. Midpoint (M) of AB, for A(-2, -3) and B(1, 2) is given as:

M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

Let A(-2, -3) = (x_1, y_1)

B(1, 2) = (x_2, y_2)

Thus:

M(\frac{-2 + 1}{2}, \frac{-3 + 2}{2})

M(\frac{-1}{2}, \frac{-1}{2})

5. Given M(3, 5) as midpoint of CD, and C(-1, -1),

let C(-1, -1) = (x_2, y_2)

D(?, ?) = (x_1, y_1)

M(3, 5) = (\frac{x_1 +(-1)}{2}, \frac{y_1 +(-1)}{2})

Rewrite the equation to find the coordinates of D

3 = \frac{x_1 - 1}{2} and 5 = \frac{y_1 - 1}{2}

Solve for each:

3 = \frac{x_1 - 1}{2}

3*2 = \frac{x_1 - 1}{2}*2

6 = x_1 - 1

6 + 1= x_1 - 1 + 1

7 = x_1

x_1 = 7

5 = \frac{y_1 - 1}{2}

5*2 = \frac{y_1 - 1}{2}*2

10 = y_1 - 1

10 + 1= y_1 - 1 + 1

11 = y_1

y_1 = 11

Coordinates of D is (7, 11)

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