coodinate geometry ( immediate help needed!)

bonkysleuth SG

in a rectangle ABCD, the coordinates of A and B are (4,2) and (2,8) respectively. given that the equation of AC is y = x - 2, find

(a)the equation of BC.

eagle SG

Because it is a rectangle ABCD, it should be clear that the line BC is perpendicular to the line AB

Gradient of AB = (8-2)/(2-4) = -3

Hence gradient of BC = 1/3

Thus, using coordinate of point B,
y - 8 = 1/3 (x - 2)

Equation of BC: y = 1/3 x + 22/3

Eagle
Owner of Strategic Tuition

bonkysleuth SG

thanks so much!

bonkysleuth SG

okay, suppose the question now wants me to find coordinates of D. can I use the fact that since the figure is a rectangle, the number of units for each opposite site is equal? Firstly, you get the coordinates of C. then you find coordinates of D by counting the number of units on the opposite site.

Is this method acceptable? or is there a way to find it? i got the answer. it's (16,6) and its correct. just wanna check whether there is any alternative to solve this question.

eagle SG

Can, but wouldn't that be a bit too troublesome?

Another method is to make use of the property of a parallelogram. Midpoint of AC = midpoint of BD.

That would be a much faster and neater way of solving.

Eagle
Owner of Strategic Tuition