Question

Show that the statement is true. If DE has endpoints (-1,6) and E (7,2), then the midpoint M of DE lies in Quadrant II.

A) M is (-4, 4)
B) M is (3, 4)
C) M is (-4, -2)
D) M is (3, -2)

Answer 1

Using the midpoint formula, the midpoint of the line segment DE with endpoints D (-1,6) and E (7,2) is found to be (3, 4), which lies in Quadrant I, not Quadrant II as the statement suggests. The statement is not true.

Step-by-step explanation:

To determine the midpoint M of the line segment DE with endpoints D (-1,6) and E (7,2), we use the midpoint formula. The formula is given by:

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

Substituting the coordinates of D (-1,6) and E (7,2) into the formula, we get:

M = ((-1 + 7)/2, (6 + 2)/2) = (6/2, 8/2)
M = (3, 4)
Now that we've found the midpoint M to be (3, 4), we need to determine which quadrant this point resides in. The point (3, 4) is in the first quadrant since both coordinates are positive. Hence, the statement 'the midpoint M of DE lies in Quadrant II' is not true. The correct answer is B) M is (3, 4), and it is located in Quadrant I.