Question

The diagram shows a rectangle ABCD. The point A is (2, 14), B is (−2, 8) and C lies on the x-axis. Find
(i) the equation of BC, (ii) find coordinates of C and D

Answer 1

Did you find point C yet?
(i.e. did you draw a picture of the rectangle?)

Answer 2

No. i have the diagram in front of me i can upload a picture so you can see

Answer 3

Are those equations for the lines accurate as labeled on the diagram?

Answer 4

yes

Answer 5

The place to start is with AB, because both of those points are given; you know, because it is a rectangle, that CD will have the same slope, so you can use that to get an equation for BC (as it is perpendicular) and use that to find the x-intercept at C.

Answer 6

Cool, then once you have point C, and you know the slope of CD (the same as AB), you can find point D - or you can use point A and the slope of AD (same as BC) to find point D.

Answer 7

point-slope form will likely be most useful
\[\large y-y_1=m(x-x_1)\]

Answer 8

thank you so much

Answer 9

im still a bit lost at point C. how do you get the x intercept?

Answer 10

^ @Zoebruwer , to get point C, use points B(-2,8) and A(2,14) to get an equation for that line. It has a slope of 3/2. Line BC is perpendicular so has a slope of -2/3. An equation for line BC can then be written using point B(-2,8) and slope = -2/3 using point-slope form,

\(\large y-y_1=m(x-x_1)\)

\(\large \rightarrow y-8=-2/3(x-(-2))\)

Putting in 0 for y in that equation will get the x-intercept.

\(\large \rightarrow 0=8 -\frac{2}{3}x-\frac{4}{3}\)

x=10.

Point C(10,0) can also be found by looking at the picture and using the slop of -2/3 to count down and over from point B. The x-axis is 8 units down, so point C must be 12 units to the right of point B. -2 + 12 = 10.