Question

The points (0,7),(5,2),(3,0) and (-2,5) are vertices of a rectangle. Determine the coordinates of the midpoints for each side and determine if the midpoint are the vertices of a rectangle.

Answer 1

To find the coordinates of the midpoints for each side of the rectangle, use the midpoint formula. The midpoints are (2.5, 4.5), (4, 1), (0.5, 2.5), and (-1, 6). The midpoints are not the vertices of a rectangle.

Step-by-step explanation:

To determine the coordinates of the midpoints for each side of the rectangle, we can use the midpoint formula. The formula for finding the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:

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

Using this formula, we can find the midpoints of the sides of the rectangle:

Midpoint of side 1: ((0 + 5)/2, (7 + 2)/2) = (2.5, 4.5)

Midpoint of side 2: ((5 + 3)/2, (2 + 0)/2) = (4, 1)

Midpoint of side 3: ((3 + -2)/2, (0 + 5)/2) = (0.5, 2.5)

Midpoint of side 4: ((-2 + 0)/2, (5 + 7)/2) = (-1, 6)

To determine if the midpoints are the vertices of a rectangle, we need to check if the opposite sides are parallel and have equal lengths. By calculating the distances between the midpoints, we can see that they are not equal, so the midpoints are not the vertices of a rectangle.