Question

The four vertices of a parallelogram are (3,2) (6,3) (9,6) and (a,B) find a and b​

Answer 1

If we label the points A(3,2) B(6,3) C(9,6) and D(a,b)
To get from A to B we can move 3 right and 1 up
If the parallelogram was labelled anticlockwise then
to get from C the D we need to go 3 left and 1 down
This would make D the point (9 - 3, 6 - 1) = (6,5)

AB || DC because both have a slope of 1/3 [because (3 - 2)/(6 - 3) = (6 - 5)/(9 - 6)]
AD || BC because both have a slope of 1 [because (5 - 2)/(6 - 3) = (6 - 3)/(9 -6)]

You could make D (12,7) but then the corners would not be labelled in order which is the accepted method
In this case the slopes of AC and BD both be 2/3 [because (6 - 2)/(9 - 3) = (7 - 3)/(12 - 6) = 4/6]

Answer 2

(15,8)

Explanation:

steps are in the picture above.

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