Hello, I just need a little assistance in Geo, my grade right now is decent(B) so I would like it to stay there, or possibly raise a little higher. If you could help me out, that'd be great. Thanks in advance :)

1. What is the area of the composite figure whose vertices have the following coordinates (-2,-2), (3,-2), (5,-4), (1,-8), (-2,-4)?

2. In the figure, TU bisects <RTS. What is the length of US?

3. The corresponding angles in triangle ABC are congruent to the corresponding angles in triangle FGH. The measures of two corresponding sides of the triangles are given.

AB=6, AC=8, FG=x+10, and FH=4x. What is the length of FH?

KenyaT.
Feb 27, 2017

#2**0 **

Kenya.....(1) can be solved with something called "Pick's" Theorem...it can be used when the vertices of a figure lie on integer values for x and y....just like yours do.....!!!

The "points" described below are the occasions where the grid lines intersect

The area is given by

Boundary points/ 2 + interior points - 1

The number of boundary points = 14

The number of interior points = 20

So

The area is

14/2 + 20 - 1 =

7 + 20 - 1 =

26 sq units

Here's a pic of the boundary points and the interior points:

CPhill
Feb 27, 2017

#4**0 **

3. The corresponding angles in triangle ABC are congruent to the corresponding angles in triangle FGH. The measures of two corresponding sides of the triangles are given.

AB=6, AC=8, FG=x+10, and FH=4x. What is the length of FH?

We have, by similar triangles, that

AB/AC = FG/FH

6 / 8 = [ x + 10] / [4x] cross-multiply

6 * 4x = 8 [x + 10 ] simplify

24x = 8x + 80 subtract 8x from both sides

16x = 80 divide both sides by 16

x = 5

So.....FH = 4(5) = 20

CPhill
Feb 27, 2017