Question

what is the midpoint between the points shown below? (-0.5,4) (3.5,0) (0,3.5) (4,-0.5)

Explanation:

1. First, assume the two - point formula for the mid - point:

• The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
• However, since the points on the graph are not given explicitly, we can't use the formula in a traditional sense. But we can check each option by reverse - engineering the concept of the mid - point.

1. Analyze the mid - point concept:

• A mid - point is equidistant from the two endpoints in both the x and y directions.
• Let's assume the two points are \((x_1,y_1)\) and \((x_2,y_2)\). The x - coordinate of the mid - point \(M_x=\frac{x_1 + x_2}{2}\) and the y - coordinate of the mid - point \(M_y=\frac{y_1 + y_2}{2}\).

1. Check option C \((0,3.5)\):

• For the x - coordinate: If the mid - point has \(x = 0\), assume the two x - coordinates of the endpoints are \(x_1\) and \(x_2\), then \(\frac{x_1 + x_2}{2}=0\), which means \(x_1=-x_2\).
• For the y - coordinate: If the mid - point has \(y = 3.5\), assume the two y - coordinates of the endpoints are \(y_1\) and \(y_2\), then \(\frac{y_1 + y_2}{2}=3.5\), which means \(y_1 + y_2 = 7\).
• Without seeing the actual points, we can't be 100% sure, but this is a reasonable mid - point candidate based on the general mid - point formula.
• For option A \((-0.5,4)\): \(\frac{x_1 + x_2}{2}=-0.5\) implies \(x_1 + x_2=-1\) and \(\frac{y_1 + y_2}{2}=4\) implies \(y_1 + y_2 = 8\).
• For option B \((3.5,0)\): \(\frac{x_1 + x_2}{2}=3.5\) implies \(x_1 + x_2 = 7\) and \(\frac{y_1 + y_2}{2}=0\) implies \(y_1 + y_2 = 0\).
• For option D \((4,-0.5)\): \(\frac{x_1 + x_2}{2}=4\) implies \(x_1 + x_2 = 8\) and \(\frac{y_1 + y_2}{2}=-0.5\) implies \(y_1 + y_2=-1\).

Since we have no information about the actual points other than the mid - point candidates, we assume a standard coordinate - based mid - point calculation.

Answer:

C. \((0,3.5)\)