Question

What is the area of a polygon with vertices of (-2, 2), (3, 2), (7, -5), and (-2, -5)?
A. 24.5 square units
B. 49 square units
C. 98 square units
D. 157.5 square units

Answer 1

@jigglypuff314

Answer 2

you are given four points
that makes it a quadrilateral
find the distance between each point
can you do that?

Answer 3

@jigglypuff314 0, 1, 2, -7?

Answer 4

not quite...
for example
(-2, 2), (3, 2)
3 - (-2) = 3 + 2 = 5
so distance between (-2, 2), (3, 2) is 5

\[distance formula: \sqrt{(x _{2}-x _{1})^{2} + (y _{2}-y _{1})^{2}} \]when given points (x1, y1) and (x2, y2)

Answer 5

@jigglypuff314 oh! I see!

Answer 6

Area of polygon by analytic geometry.
Each line is obtained by x(n)*y(n+1)-x(n+1)*y(n).
Add up values of all lines, divide by two (ignore sign).
Works for triangles, quads, and any other polygon.
(-2, 2) -2*2-3*2=-10
(3, 2) 3*(-5)-7(2)=-29
(7, -5) 7*(-5)-(-2)(-5)=-45
(-2, -5) (-2)*2-(-2)(-5)=-14
(-2,2) (repetition of first point)
Add up each line's worth and divide by 2 to get 98/2=49 (ignore sign)

Answer 7

@mathmate thank you so much! can you help me with another?

Answer 8

Just post your problem and I'll try.

Answer 9

If the figure below has rotational symmetry, find the angle of rotation about the center that results in an image that matches the original figure.

Answer 10

A. 90
B. 120
C. 210
D. no rotational symmetry

Answer 11

How many sectors are there?

Answer 12

@mathmate 4?

Answer 13

What is the angle of each of the 4 arcs?

Answer 14

@mathmate obtuse?

Answer 15

The angle in degrees.

Answer 16

@mathmate If you look at it, they almost look like 90 degree angles from a certain point of view

Answer 17

How can you be sure, assuming all 4 arcs are equal, and one comlete turn equals 360 degrees?

Answer 18

@mathmate I'm really not sure, this entire question confuses me.

Answer 19

Are you familiar with that?

Answer 20

@mathmate yes

Answer 21

So if there are 4 equal sectors, what is the size of each central angle?

Answer 22

@mathmate 90?

Answer 23

There you go!
So how many degrees do you need to turn the circle to make it look like before?

Answer 24

@mathmate what do you mean?

Answer 25

"If the figure below has rotational symmetry, find the angle of rotation about the center that results in an image that matches the original figure. "

Rotational symmetry means that by turning an angle less than 360, you end up with the (apparently) the same shape as before.

See drawing above.
Rotating 90 degrees gives a shape the same as no rotation. This is called rotational symmetry. This is the angle you are asked to find.

Answer 26

@mathmate oh! so its 90?

Answer 27

You are looking for the smallest angle of rotation to make it look like the original. Yes, it is 90 degrees.

Answer 28

@mathmate thank you very, very much. could you by any chance check some of my answers for me?

Answer 29

I certainly can.
Have they been posted?

Answer 30

Not yet, I'll write them right now.

Answer 31

An airplane pilot over the Pacific sights an atoll at an angle of depression of 7 degrees. At this time, the horizontal distance from the airplane to the atoll is 3,729 meters. The diagram is not drawn to scale. What is the height of the plane to the nearest meter?
A. 458 meters
B. 454 meters
C. 3,667 meters
D. 3,701 meters

Answer 32

What is your answer?

Answer 33

I went with A.