## anonymous 4 years ago Can any one help with this? I am just stumped on this problem! plot each point and form the triangle ABC. Verify that the triangle is a right triangle. Find its area. A =(4, −3); B =(4, 1); C = (2, 1)

1. anonymous

thats it roughly find lengths of the 3 sides and Check that AC^2 = AB^2 + BC^2 so proving ABC is rt angled

2. anonymous

No negative x values here, but not that important

3. anonymous

oh - right - i messed up there1

4. anonymous

The distance formula is $d=\sqrt{(y2-y1)+(x2-x1)}$ You don't need to find the square root though because you're just going to be squaring them again when using the Pythagorean theorem.

5. anonymous

for example BC^2 = 0^2 + (4-2)^2 = 4

6. anonymous

Thanks guys :)

7. anonymous

|dw:1328130277370:dw|

8. anonymous

yw

9. amistre64

we could also create 3 vectors and dot them to see if any 2 vectors = 0

10. anonymous

This like a different language to me when it comes to math. lol What do you mean?

11. anonymous

you need to know something about vectors to understand what amis said it would take too long to explain here - briefly when two vectors are multiplied (or 'dotted'), if the answer is zero then they are at right angles to each other.

12. anonymous

I see...that is a little confusing to me right now.

13. anonymous

Is this correct or am I way off? D(A,B)=sqrt (4-4)^2+(-3-1)^2=0+16= 16 D(B,C)=sgrt (4-2)^2(1-1)^2=4+0=4 D(A,C)=sqrt (4-2)^2+(-3-1)^2=4+16=20 D(A,B)^2+(B,C)^2=16^2+4^2=256+16=272 D(A,C)=20^2= 400 D(A,B)^2+D(B,C)^2 does not equal D(A,C)^2 It is not a right triangle

14. anonymous

A =(4, −3); B =(4, 1); C = (2, 1) If ABC is a right triangle, $d(AC)^2=d(AB)^2+d(BC)^2$ You can go without using the square root of the distance formula here because you will be later squaring that distance when plugging it into the Pythagorean theorem. $d^2=(\sqrt{(y2-y1)^2+(x2-x1)^2})^2=(y2-y1)^2+(x2-x1)^2$ So you can evaluate thisand see if it results in a true answer: $[(1+3)^2+(2-4)^2]=[(1+3)^2+(4-4)^2]+[(1-1)^2+(4-2)^2]$ $4^2+(-2)^2=4^2+0^2+0^2+2^2$ $20=16+4$ This expression is TRUE; therefore, it is a right triangle.

15. anonymous

Thank you for all the help :) I finally figured it out!!