Final answer:
To complete rectangle LMNP with an area of 700 square units, given the coordinates of L and P, we calculate the length as 35 units and the width as 20 units. The y-coordinates of M and N must be 20 units away from L and P, respectively. Option a) satisfies the conditions with M = (-10, 30), N = (10, 0).
Step-by-step explanation:
The question asks us to determine the coordinates of points M and N that would complete the rectangle LMNP with an area of 700 square units. Given the coordinates L(15, 15) and P(-20, 15), we can infer that LP is the top side of the rectangle parallel to the x-axis, and since both points have the same y-coordinate (15), the length of LP is the absolute difference in their x-coordinates, which is |15 - (-20)| = 35 units.
The area of a rectangle is calculated by the formula Area = length × width. Since we know the length is 35 units and the area is 700 square units, we can find the width by dividing the area by the length, which gives us a width of 700 / 35 = 20 units.
Therefore, the y-coordinates of M and N should be 20 units away from L and P, respectively. L and P are at y-coordinate 15, so M and N must be at y = 15 ± 20. That means y-coordinate of M or N can be either -5 or 35. By looking at the given options, only option a) M = (-10, 30), N = (10, 0) has both a y-coordinate of -5 or 35 for M and N and is consistent with the width of the rectangle.