Question

Leanne plotted the points (2, 1), (6, 1), and (8, 6) on a coordinate plane. Which ordered pair should Leanne plot next to complete a parallelogram?

a. (4, 6)
b. (8, 1)
c. (2, 6)
d. (10, 1)

Answer 1

To complete a parallelogram with given points, the opposite sides should have the same length. For the given points (2, 1), (6, 1), and (8, 6), the ordered pair that Leanne should plot next to complete the parallelogram is (4, 6). Hence the correct answer is option A

Step-by-step explanation:

To complete a parallelogram, the opposite sides should have the same length. Looking at the given points, we can see that the line segment connecting (2, 1) and (6, 1) has a length of 4 units. The line segment connecting (8, 6) and the unknown point, let's call it (x, y), should also have a length of 4 units.

Using the distance formula, we can calculate the distance between (8, 6) and (x, y):

d = sqrt((x - 8)^2 + (y - 6)^2)

Equating this distance to 4, we get:

sqrt((x - 8)^2 + (y - 6)^2) = 4

Simplifying this equation, we find two possible solutions for (x, y): (4, 6) or (12, 6).

So the ordered pair that Leanne should plot next to complete a parallelogram is (4, 6).

Hence the correct answer is option A