Question

What value of X and y guarantee that ABCD Is a parallelogram

Answer 1

Answer:

We can mark A(-2,1) and D(1,2) on a graph sheet.

Now B(x,0) lies on the x axis while C (4,y) lies on a line parallel to y axis passing through (4,0)

Distance AD = sqrt((-2–1)^2 + (1–2)^2) = sqrt(10)

= Distance BC as it is the opposite side of the parallelogram

Therefore sqrt((x-4)^2 + (0-y)^2) = sqrt(10)

(x-4)^2 +y^2 = 10 ….(1)

Slope of AD is (2–1)/(1+2) = 1/3 = slope of BC as opposite sides are parallel

Therefore (y-0)/(4-x) = 1/3

Or, 3y = 4 - x …(2)

Using it in (1) we get,

10y^2 = 10

y^2 = 1

y = +1 or -1

Correspondingly

x = +1 or +7

B1(1,0) and C1(4,1) are the other two points of the parallelogram AB1C1D

OR

B2(7,0) and C2(4,-1) are the other two points of the parallelogram AC2B2D

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Answer 2

Answer:

x=6°

y=7°

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