+0  
 
+5
274
6
avatar+51 

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
Sort: 

6+0 Answers

 #1
avatar
0

the length of FH is 2

Guest Feb 27, 2017
 #2
avatar+79689 
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:

 

 

cool cool cool

CPhill  Feb 27, 2017
 #3
avatar+51 
0

Thanks so much, although I had 26 already as my answer. I guess I was overthinking it.

KenyaT.  Feb 27, 2017
 #4
avatar+79689 
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

 

 

 

cool cool cool

CPhill  Feb 27, 2017
 #5
avatar+79689 
0

Actually....you probably divided the figure into a trapezoid and a triangle or as a rectangle and two triangles??....I just thought  it might be kinda' neat to show you another way.....plus.....it gives me a chance to "show off"....LOL!!!!

 

 

cool cool cool

CPhill  Feb 27, 2017
 #6
avatar+51 
0

lol, well obviously you're good at math

KenyaT.  Feb 27, 2017

28 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details