Question

Use the graph of $\triangle ABC$ with midsegments $\overline{DE},\ \overline{EF},\ $ and $\overline{DF}$ . Find the coordinates of points $D$ , $E$ , and $F$ .

A triangle is drawn on coordinate plane. The x-axis is extended from negative 6 to 2, in increments of 2. The y-axis is extended from negative 6 to 2, in increments of 2. Vertex A lies at the ordered pair negative 5 comma 2. Vertex B lies at the ordered pair 1 comma negative 2. Vertex C lies at the ordered pair negative 3 comma negative 6. E is the midpoint of side A B. D is the midpoint of side A C. F is the midpoint of side B C. Segments D E, E F, and D F are the mid-segments.

$D$ (
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), $E$ (
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), $F$ (
,
)
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Answer 1

The coordinates are: D is
`$(-4, -2)$`, E is
`$(-2, 0)$`, F is
`$(-1, -4)$`

To find the coordinates of points D, E, and F which are midpoints of the sides of
`$\triangle ABC$`, we can use the midpoint formula. The midpoint formula for a line segment with endpoints
`$(x_1, y_1)$` and
`$(x_2, y_2)$` is given by:

`\[ \left((x_1 + x_2)/(2), (y_1 + y_2)/(2)\right) \]`

Let's apply this formula to find the coordinates:

1. Coordinates of D (midpoint of side AC):

`\[ D = \left((x_A + x_C)/(2), (y_A + y_C)/(2)\right) = \left((-5 + (-3))/(2), (2 + (-6))/(2)\right) = (-4, -2) \]`

2. Coordinates of E (midpoint of side AB):

`\[ E = \left((x_A + x_B)/(2), (y_A + y_B)/(2)\right) = \left((-5 + 1)/(2), (2 + (-2))/(2)\right) = (-2, 0) \]`

3. Coordinates of F (midpoint of side BC):

`\[ F = \left((x_B + x_C)/(2), (y_B + y_C)/(2)\right) = \left((1 + (-3))/(2), ((-2) + (-6))/(2)\right) = (-1, -4) \]`

So, the coordinates are:

- D is
`$(-4, -2)$`

- E is
`$(-2, 0)$`

- F is
`$(-1, -4)$`

The probable question may be: "Use the graph of $\triangle ABC$ with midsegments $\overline{DE},\ \overline{EF},\ $ and $\overline{DF}$. Find the coordinates of points D, E, and F.

A triangle is drawn on coordinate plane. The x-axis is extended from negative 6 to 2, in increments of 2. The y-axis is extended from negative 6 to 2, in increments of 2. Vertex A lies at the ordered pair negative 5 comma 2. Vertex B lies at the ordered pair 1 comma negative 2. Vertex C lies at the ordered pair negative 3 comma negative 6. E is the midpoint of side A B. D is the midpoint of side A C. F is the midpoint of side B C. Segments D E, E F, and D F are the mid-segments. Find the coordinates of point D,E,F"