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Ava wants to draw a parallelogram on the coordinate plane. She

plots these 3 points.

Part A
Find and label the coordinates of the fourth vertex, K, of the
parallelogram. Draw the parallelogram.

Part B
What is the length of side JK? How do you know?​

1 Answer

6 votes

Answer:


k =(2,1)


JK = 2

Explanation:

Given


J = (0,1) ----
(x_1,y_1)


H = (1,-2) ---
(x_2,y_2)


I = (3,-2) ---
(x_3,y_3)

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:


(1)/(2)(I + J) = (1)/(2)(H+K)


(1)/(2)(x_3+x_1,y_3+y_1) = (1)/(2)(x_2+x,y_2+y)


(1)/(2)(3+0,-2+1) = (1)/(2)(1+x,-2+y)


(1)/(2)(3,-1) = (1)/(2)(1+x,-2+y)

Multiply through by 2


(3,-1) = (1+x,-2+y)

By comparison:


1 + x = 3


-2 + y = -1

Solve for x and y


x = 3 - 1 =2


y = -1 +2 = 1

So, the coordinates of k is:


k =(2,1)

The length of JK is calculated using distance (d) formula


d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2


J = (0,1) ----
(x_1,y_1)


k =(2,1) ----
(x_2,y_2)

So:


d = \sqrt{(0 - 2)^2 + (1 - 1)^2


d = \sqrt{(- 2)^2 + (0)^2


d = \sqrt{4 + 0


d = \sqrt{4


d = 2

Hence:


JK = 2

Ava wants to draw a parallelogram on the coordinate plane. She plots these 3 points-example-1
User Meanman
by
6.4k points
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