Question

Sheila wants to draw a rectangle that has a perimeter of 28 units. She placed two of the vertices of the rectangle at (-1,5) and (-1,-3). Where could she place the other vertices?

a) (5,-3) and (5,5)
b) (3,-3) and (3,5)
c) (-3,-3) and (-3,5)
d) (-5,-3) and (-5,5)

Answer 1

To find the remaining vertices of the rectangle, given a height of 8 units from (-1,5) to (-1,-3) and a perimeter of 28 units, we calculate the length to be 6 units. By moving horizontally 6 units to the right from the original vertices, we find the coordinates (5,-3) and (5,5), corresponding to option (a).

Step-by-step explanation:

Sheila wants to draw a rectangle that has a perimeter of 28 units. She placed two of the vertices at (-1,5) and (-1,-3), which are vertically aligned, indicating these are the height points of the rectangle. Since the distance between these points is 8 units, the height of the rectangle is 8 units. The formula for the perimeter of a rectangle is P = 2(length + height). Given that the perimeter P is 28 units and the height is 8 units, we can substitute and find the length:

28 = 2(length + 8)
14 = length + 8
length = 14 - 8
length = 6 units

Knowing that the length of the rectangle is 6 units, we can find the coordinates for the remaining two vertices by moving 6 units horizontally from the existing vertices. Since the original vertices have x-coordinates of -1, we obtain the x-coordinates for the remaining vertices by adding 6, which results in -1 + 6 = 5. Therefore, the correct coordinates for the remaining vertices are (5,-3) and (5,5), which match option (a).