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# analytic geometry

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The line 2x + 3y = 6 meets the y-axis at A and the x-axis at B. C is the point such thatAB = BC. CD is drawn perpendicular to AC to meet the line through A parallel to 5x + y = 7 at D.

a. Find the coordinate of A, B and C.

b. State the equations of CD and AD and hence find the coordinates of D.

c. Calculate the area of the triangle ACD.​

Mar 20, 2021

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To start this problem out, we will find the x and y-intercepts of 2x + 3y = 6. The x-intercept is found when y is 0. So, we plug zero into the equation to get:

2x + 3(0) = 6

2x = 6

x = 3

So now we know that the coordinates of the x-intercept is 3. (this point is b)

The y-intercept is found when x = 0. So, we do the same thing as before, except x = 0.

2(0) + 3y = 6

3y = 6

y = 2

So now we know that the coordinates of the y-intercept is 2. (this point is a)

This is as far as I will go, as the rest of the problem seems a little too complicated and confusing for my 2 little brain cells. Hope this helped though!

Mar 20, 2021