Question

Calculate the area of triangle ABC with altitude CD, given A (-7, -1), B (-1, 5), C (0, 0), and D (-3, 3).

Answer 1

9 square units
18 square units
18.5 square units
21 square units

Answer 2

@mathstudent55

Answer 3

Did you figure this one out (hence closure)?

Answer 4

No @AccessDenied

Answer 5

Alright.

Well, you want to find Area. That entails knowing two things to apply this area formula:
\( A_{\text{triangle}} = \frac{1}{2} b h \)
The base, and the height.

Answer 6

Yes.

Answer 7

So, we have the three vertices of the triangle. We also have this extra D coordinate which gives an altitude. According to the definition of an altitude, though, that is pretty much the height of the triangle assuming the side perpendicular is the base, correct?

Answer 8

Yes. Correct.

Answer 9

So, if you have trouble visualizing which side is perpendicular, I would recommend simply plotting the points and seeing it for yourself. But CD is our altitude and also our height. The side opposite of vertex C is the segment AB.

Answer 10

...Okay that's also good. :p

Answer 11

Okay.

Answer 12

So the final goal is to find the length of CD, the height, and AB, our base.
Then they are plugged right in to our Area formula.

Answer 13

CD ; 4.25

Answer 14

AB ; 8.50

Answer 15

I am not familiar with GeoGebra or if it allows you to find the lengths freely. Otherwise, distance formula between the two points works too.
In either case, though, whichever is appropriate for your needs. :)

Answer 16

So the Area is then:
A = 1/2 * AB * CD

Answer 17

18...

Answer 18

Correct?

Answer 19

18.0625.. seems close enough to 18 to not be 18.5.

Answer 20

So, correct.
(Had to check with distance formula to make sure... with the exact measurements, you get exactly 18)

Answer 21

Yeah thats what i got thanks! I have some more can you help?

Answer 22

Find the perimeter of a quadrilateral with vertices at R (-2, 1), S (-5, 5), T (2, 5), U (5, 1). Round your answer to the nearest hundredth when necessary.


22 units
24 units
28 units
36 units

Answer 23

Perimeter means the length around the figure. You have the coordinates, and you want to find the lengths or distances of each pair of points creating a side of the quadrilateral.

Answer 24

Yes i got that.

Answer 25

You might be alright to assume it goes in order: R connects to S, S connects to T, T connects to U, and U loops back on R. A plot will confirm whether that is true or not.

Answer 26

24 units

Answer 27

Looks good to me. Indeed, that assumption is true; RSTU is in order.

Answer 28

For the line segment whose endpoints are A (0, 0) and B (4, 3), find the x value for the point located 2/3 the distance from A to B.
2.2
2.7
3.3
3.5

Answer 29

Well, it would be good to start with finding the distance.

Then we can take 2/3 of it for the length of this segment:

Answer 30

2.7..?

Answer 31

2.7 seems to be correct.

Those would make for similar triangles, so hypotenuse ratio = x-length ratio
4/x = 5/ (5 (2/3))
x = 4 * 2/3

Answer 32

Point L is located at (4, -3) and M is located at (-8, 5). Find the y value of the point that lies halfway between L and M.

1.5
4
3.5
1

Answer 33

So, we want the midpoint of L and M.
You know how to find the midpoint of two given points?

Answer 34

Yes i just can't remember at the moment..

Answer 35

The easiest way to remember it is the average of the corresponding coordinates.

Add the two x-values and divide by 2 for the midpoint x-coordinate
Add the two y-values and divide by 2 for the midpoint y coordinate

Answer 36

Wow thats a great way to remember actually

Answer 37

Answer is 1..?

Answer 38

Correct. :)

Answer 39

A segment with endpoints I (5, 2) and J (9, 10) is divided by a point K such that IK and IJ form a 2:3 ratio. Find the y value for K.

4.6
5.4
4.8
5.2

Answer 40

So, the two sides make the ratio: IK / IJ = 2 / 3
We could find the distance between K(x, y) and I(5, 2) along with the distance between K(x, y) and J(9, 10). Then we could intersect with the line through the two points I and J.
This problem seems more involved...

Answer 41

In both cases, you would use distance formula of the two points:
\( d = \sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Answer 42

input them?

Answer 43

Hang on, I was thinking KI and KJ. Sorry.
Let me rethink that.

Answer 44

sure no problem..

Answer 45

So the statement IK : IJ = 2 : 3 implies that IK is 2/3 the length of IJ.
So we are finding the point K whose distance from I is 2/3 IJ.

Answer 46

Yes.

Answer 47

So we would still find the length of IJ which would lead us the length of IK. Then we just need to find the point 2/3 IJ away from I. The geometric argument is that we are swiping a circle of radius 2/3 IJ with center at I around and trying to find the place where the line IJ intersects the circle.