Question

PLEASE HELP
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Answer 1

The endpoint coordinates for the midsegment of triangle BCD that is parallel to BC are (-2, -1) and (1, 0).

How to find the endpoint coordinates for the midsegment of a triangle?

Given the triangle BCD, the midsegment's endpoint can be calculated by finding the midpoint between sides BD and CD, which is parallel to side BC.

Using the midpoint formula, find the midpoints between B(-3, 1) and D(-1, -3):

The midpoint formula is given by:
`\[ M = \left( \frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2} \right) \]`

Where
`(x_1, y_1)` and
`(x_2, y_2)` are the coordinates of the two points.

For the points B(-3, 1) and D(-1, -3), the midpoint M can be calculated as follows:

`\[ M_x = \frac{{-3 + (-1)}}{2} \]`

`\[ M_y = \frac{{1 + (-3)}}{2} \]`

Solving these equations:

`\[ M_x = \frac{{-4}}{2} = -2 \]`

`\[ M_y = \frac{{-2}}{2} = -1 \]`

So, the midpoint M between B and D is (-2, -1).

Using the midpoint formula, find the midpoints between C(3, 3) and D(-1, -3):

For the points C(3, 3) and D(-1, -3), the midpoint (M) can be calculated as follows:

`\[ M_x = \frac{{3 + (-1)}}{2} \]`

`\[ M_y = \frac{{3 + (-3)}}{2} \]`

Solving these equations:

`\[ M_x = \frac{{2}}{2} = 1 \]`

`\[ M_y = \frac{{0}}{2} = 0 \]`

So, the midpoint M between C and D is (1, 0).

The endpoints are therefore (-2, -1) and (1, 0).