Calculate the area of triangle CDE with altitude EF, given C (3, −2), D (−1, 2), E (2, 3), and F (0, 1). can someone hel me

Question

Calculate the area of triangle CDE with altitude EF, given C (3, −2), D (−1, 2), E (2, 3), and F (0, 1).  can someone hel me

anonymous · Answer

help me please

jim_thompson5910 · Answer

hint: find the length of CD. This is the base b of the triangle. Then find the altitude EF. This is the height h of the triangle. 

Once you have those 2 pieces of info, you use the formula

A = (b*h)/2

jim_thompson5910 · Answer

Let me know if that helps or not

anonymous · Answer

it helped a lil but not that much can you tell me more please

jim_thompson5910 · Answer

To find the length of CD and EF, you use the distance formula

$$\Large d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$

jim_thompson5910 · Answer

Finding the length of CD

Let 

C = (3,-2) = (x1,y1)

so

x1 = 3
y1 = -2


D = (-1,2) = (x1,y1)

so

x2 = -1
y2 = 2


Plug all this in to get...


$$\Large d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$


$$\Large d = \sqrt{(3-(-1))^2+(-2-2)^2}$$


$$\Large d = \sqrt{(3+1)^2+(-2-2)^2}$$


$$\Large d = ???$$

anonymous · Answer

ok i understand how to do that but theres four coordinates these are the answers 

 4 square units 

6.2 square units 

8 square units 

8.7 square units
 im thinking b though

jim_thompson5910 · Answer

what's the length of CD?

jim_thompson5910 · Answer

in radical form

anonymous · Answer

32 so then you square root it?

anonymous · Answer

is that rite?

jim_thompson5910 · Answer

good, so CD is $\Large \sqrt{32}$ units long. This is the length of the base. What's the height?

anonymous · Answer

how do i do that now? i need to do the same thing again?

jim_thompson5910 · Answer

yes, but now using points E and F

jim_thompson5910 · Answer

since EF is the altitude (ie height) for base CD

anonymous · Answer

ok so now i got 20 what do i do now?

jim_thompson5910 · Answer

that is incorrect

jim_thompson5910 · Answer

we have E (2, 3), and F (0, 1)

so make

(x1,y1) = (2,3)
(x2,y2) = (0,1)

jim_thompson5910 · Answer

tell me what you get when you plug that into 

$$\Large d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$

anonymous · Answer

oohhh im sorry i got 8 now

anonymous · Answer

now wat do i do?

jim_thompson5910 · Answer

should be $\Large \sqrt{8}$

jim_thompson5910 · Answer

$$\Large A = \frac{b*h}{2}$$


$$\Large A = \frac{(\sqrt{32})*(\sqrt{8})}{2}$$


$$\Large A = ???$$

anonymous · Answer

ok so its 8?

jim_thompson5910 · Answer

Correct, the answer is 8 square units