Question

Calculate the area of triangle ABC with altitude CD, given A (-6, -1), B (-1, 5), C (0, 0), and D (-2, 3).

Answer 1

a. 14.1 square units
b. 18 square units
c. 19.5 square units
d. 21 square units

Answer 2

odd question

Answer 3

How so?

Answer 4

what does the altitude mean? is there a third dimension? if so it wouldn't be a triangle and would be some type of pyramid.

Answer 5

ok I think I might be seeing it

Answer 6

No it's a 2-dimensional shape... the altitude es the "perpendicular segment from a vertex to its opposite side".

Answer 7

yes, the picture looks like an accurate drawing of an altitude. what I don't get is that when I graph this particular triangle, the altitude doesn't fall into line with the other side.

Answer 8

So you need to know the formula \[\frac{ 1 }{ 2 }bh=\frac{ 1 }{ 2 }|[-1-(-6),5-(-1)][-2,3]|\]

Answer 9

Oh gosh... what do all the numbers represent?

Answer 10

the absolute value || bars in this case mean find the magnitude of the vectors

Answer 11

so you need to find the magnitude of side AB and CD

Answer 12

You can do this by using the distance formula
\[d=\sqrt{(y _{2}-y _{1})^{2}+(x _{2}-x _{1})^{2}}\]

Answer 13

I haven't learned any of this... can you walk me through the steps?

Answer 14

so
\[d=\sqrt{(5-(-1))^{2}+(-1-(-6))^{2}}=\left| AB \right|\]

Answer 15

36 + 25 = 61 ... sqrt(61) = 7.81

Answer 16

That isn't one of the options..

Answer 17

yes you got it. That is the value for the base

Answer 18

Now do the same thing for angle CD

Answer 19

or side CD excuse me

Answer 20

so side CD is simpler since C is (0,0)

Answer 21

\[d= \sqrt{3^{2}+(-2)^{2}}\]

Answer 22

that is the value for side CD

Answer 23

Okay so it would be 4 + 9 = 13 sqrt13 = 3.6

Answer 24

yes correct

Answer 25

Now do I multiply 7.81 and 3.6?

Answer 26

now ,multiply the two numbers together and multiply by 1/2

Answer 27

this is from the formula \[\frac{ 1 }{ 2 }bh\]

Answer 28

14.1?

Answer 29

That's it

Answer 30

Now did that make any sense?

Answer 31

probably not

Answer 32

Thank you!!

Answer 33

Yes, I think I get it. I was just confused because when I graphed it, the altitude didn't line up.

Answer 34

Basically a summary is you need to find the magnitude of the base and the altitude and use the formula for finding the area of a triangle

Answer 35

ty :)

Answer 36

long story short

Answer 37

you're welcome