Question

AXYZ has vertices X(-5, -2), Y( -3, 4), and Z(3, 0). Find the coordinates of the vertices of the midsegment triangle of AXYZ.

Vertex on XY:
Vertex on YZ:
Vertex on XZ:

Answer 1

The coordinates of the midsegment triangle of AXYZ are (-4, 1), (0, 2), and (-1, -1).

Step-by-step explanation:

The midsegment triangle of AXYZ is formed by connecting the midpoints of the sides of the triangle AXYZ. To find the coordinates of the midsegment triangle, we need to find the midpoints of each side of the triangle.

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:

(x, y) = ((x1 + x2)/2, (y1 + y2)/2)

Using this formula, we can find the coordinates of the midpoints:

• Vertex on XY: ((-5 + -3)/2, (-2 + 4)/2) = (-4, 1)
• Vertex on YZ: ((-3 + 3)/2, (4 + 0)/2) = (0, 2)
• Vertex on XZ: ((-5 + 3)/2, (-2 + 0)/2) = (-1, -1)

Answer 2

The vertices of the midsegment triangle of ΔXYZ with vertices X(-5, -2), Y(-3, 4), and Z(3, 0) are found at (-4, 1) for XY, (0, 2) for YZ, and (-1, -1) for XZ by calculating the midpoints of each side of the triangle.

Step-by-step explanation:

To find the coordinates of the vertices of the midsegment triangle of ΔXYZ, we need to calculate the midpoints of each side of the triangle. The midsegment of a triangle connects the midpoints of two sides and is parallel to the third side.

• Vertex on XY: We calculate the midpoint between X(-5, -2) and Y(-3, 4). Using the midpoint formula, which is ((x1 + x2)/2, (y1 + y2)/2), we get the following coordinates: ((-5 - 3)/2, (-2 + 4)/2), which simplifies to (-4, 1).
• Vertex on YZ: For the midpoint between Y(-3, 4) and Z(3, 0), apply the midpoint formula to get ((-3 + 3)/2, (4 + 0)/2), resulting in (0, 2).
• Vertex on XZ: The midpoint between X(-5, -2) and Z(3, 0) is found with the formula, resulting in ((-5 + 3)/2, (-2 + 0)/2), which is (-1, -1).

Therefore, the coordinates of the vertices of the midsegment triangle are (-4, 1), (0, 2), and (-1, -1).