Area with Vertices?

You don't have to answer/work out the problem.

Just tell me how to set it up please.



We did this at the beginning of the school year, and I can't find it in our book.



A rose garden is being planted as a border around two sides f a triangular shaped lawn in a city park. Two of the vertices of the triangular lawn have coordinates (-2.4) and (3, -5). The gardener wishes to locate the third vertex so that the 1 lawn's area is 25 square feet. Find the value of f if the coordinates of the third vertex are (3, f).

Area with Vertices?
Since the third vertex is to be (3, f), one of the sides is along the vertical line x = 3. Take this side (length f+5) as base, and then the height is 5 (horizontal distance between the line x=3 and the point (-2, 4))

Area of triangle = 0.5*base*height

and since height = 5 you just have to choose the value of f to make the base have the value that gives area 25. (see how carefully I avoid getting the answer!)