Answer:
[tex]C = (30,500)[/tex]
Step-by-step explanation:
Given
[tex]Area = 1800ft^2[/tex]
[tex]A = (6,0)[/tex]
[tex]B = (0,25)[/tex]
[tex]C(x,y) = (30,y)[/tex]
Required
Determine the coordinates of C
The area of triangle is calculated as thus:
[tex]Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}[/tex]
This gives:
[tex]1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}[/tex]
[tex]1800= \frac{|6(25 - y) + 30(0- 25)|}{2}[/tex]
[tex]1800= \frac{|6(25 - y) + 30(-25)|}{2}[/tex]
[tex]1800= \frac{|150 - 6y -750 |}{2}[/tex]
[tex]1800= \frac{|150 -750- 6y |}{2}[/tex]
[tex]1800= \frac{|-600- 6y |}{2}[/tex]
Multiply through by 2
[tex]2 * 1800= |-600- 6y|[/tex]
[tex]3600= |-600- 6y|[/tex]
[tex]3600= |-(600+ 6y)|[/tex]
[tex]3600= 600+ 6y[/tex]
Solve for 6y
[tex]6y = 3600 - 600[/tex]
[tex]6y = 3000[/tex]
Solve for y
[tex]y = 3000/6[/tex]
[tex]y = 500[/tex]
Hence:
The point is:
[tex]C = (30,500)[/tex]
