Question

A triangle has vertices at (2, 3), (½ , –2), and (– 3, 2). What is the area of the triangle? please show me the steps

Answer 1

no

Answer 2

Please can you explain

Answer 3

Just use the formula 1/2(x1 y2 + x2 y3 + x3y1- x2y1-x3y2-x1y3)

Answer 4

Otherwise do you know distance formula?

Answer 5

And how to calculate distance of a point from a line?

Answer 6

yes .I do

Answer 7

Ah ok. So lets use co ordinate geometry . Can you tell me equation of line passing through (1/2,-2) and (3,-2)?

Answer 8

And (-3,2) sorry

Answer 9

chealsea rules.

Answer 10

of course it does(but thats irrevelant to finding area of a triangle. :P)

Answer 11

y=-8/7x-10/7

Answer 12

Ok I'll assume you did that correctly. Now find distance of (2,3) from this line.

Answer 13

please can you explain me how to

Answer 14

Ok Suppose i have a line ax+by+c=0. And a point h,k. Then disatnce of point from this line would be
(ah+bk+c)/sqrt(a^2+b^2). If you get negative value just make it positive by removing minus sign.

Answer 15

understood?

Answer 16

no. I didn't

Answer 17

You did not understand the formula? Damn.
Ok In your case the line is 7y+8x+10=0. And the point is 2,3.
Si a=7,b=8,c=10. h=2,k=3. Using the formula you get
(7*2+8*3+10)/sqrt(64+49)=48/sqrt(113).

Answer 18

Now is it a little bit clearer?

Answer 19

yes

Answer 20

good, now find distance AB.

Answer 21

Then just do 1/2 * AB * 48/sqrt(113).

Answer 22

answer is 47/4. Thanks for helping