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Question

In parallelogram ABCD, A(3,2), B(8,4) and D(5,7). Then the coordinates of C is


A

(9,8)

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B

(10,9)

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C

(9,10)

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D

(8,9)

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Solution

The correct option is B

(10,9)


Draw AE, DF parallel to x-axis and BE, CF parallel to y-axis, as shown in the figure above.

Now, in right triangles ABE and DCF,

AB = DC

BAE = CDF

ABE = DCF

Therefore, AE = DF and BE = CF

Hence AE = DF = 8 -3 = 5 and BE = CF = 4 - 2 = 2

Now, x-coordinate of C = 5 + DF = 5 + 5 = 10

y-coordinate of C = 7 + CF = 7 + 2 = 9

Therefore coordinates of C is (10,9).


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