## anonymous one year ago The diagram shows a rectangle ABCD. The point A is (2,14). B is (-2,8) and C lies on the x-axis (?,0) Find the equation of BC. the coordinates of C and D.

1. anonymous

One second, I have done some work, just trying to find the coordinates for C and D. Missing X values.

2. anonymous

y-8= -2/3 (x+2) for BC equation. C (?,0) D (?,6) Not sure what to do. I did slope equation. 14-8/2+2 = 6/4 3/2 then opp slope recip. -2/3

3. anonymous

okay @.@ may i ask what are the question that you want to ask @.@

4. anonymous

How to find the x values for those coordinates. :p

5. anonymous

okay can you show me how you got those answers up there? cuz i confuse by your own answers and question @.@

6. anonymous

Apologies, I have a packet with an image. My answers are accurate, which I am completely confident of.

7. anonymous

@iYuko

8. jim_thompson5910

The equation of line BC, in point slope form, is $$\Large y - 8 = -\frac{2}{3}(x+2)$$. In slope-intercept form, the equation is $$\Large y= -\frac{2}{3}x+\frac{20}{3}$$ It doesn't matter which equation you use. Plug in y = 0 and solve for x to get the x coordinate of point C.

9. anonymous

Can you explain to me how you got 20/3? @jim_thompson5910

10. anonymous

Oh, I see, for some reason I attempted to use outside numbers to distribute, I completely understand what I did wrong, thank you so much!

11. jim_thompson5910

Sure. Here are the steps I did to convert from point slope form to slope intercept form. $\Large y - 8 = -\frac{2}{3}(x+2)$ $\Large y - 8 = -\frac{2}{3}(x)-\frac{2}{3}(2)$ $\Large y - 8 = -\frac{2}{3}x-\frac{4}{3}$ $\Large y - 8+8 = -\frac{2}{3}x-\frac{4}{3}+8$ $\Large y = -\frac{2}{3}x-\frac{4}{3}+8$ $\Large y = -\frac{2}{3}x-\frac{4}{3}+8*\frac{3}{3}$ $\Large y = -\frac{2}{3}x-\frac{4}{3}+\frac{24}{3}$ $\Large y = -\frac{2}{3}x+\frac{-4+24}{3}$ $\Large y = -\frac{2}{3}x+\frac{20}{3}$