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.
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!