Question

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and
F(4, -1)?

Answer 1

u can get it by drawing these points to there x and y coordinates

Answer 2

first we draw it if it obvious then we have the answer if we didnt got it yet then u would move to plan b

Answer 3

soo now we have to find all the length of the three lines we have DE DF and FE
if we have two points and we want to have the length of the line between them we use this rule
\[L=\sqrt{(X _{2}-X _{1})^{2} + (Y _{2}-Y _{1})^{2}}\]

Answer 4

i will do one and u do the rest i will leave the finall answers soo u can make sure
lets say we need to find the length of line DE
DE=\[\sqrt{(8-7)^{2} + (1-3)^{2}}= \sqrt{5}\]

Answer 5

and like with we get DF= 5
EF= \[2\sqrt{5}= 2.1147\]

Answer 6

now we define what that triangle is if the square of largest line equlas the squares of the other two lines then this triangle is right angled
if it is bigger than them it is Obtuse triangle
if it is smaller than them it is Acute-angled triangle

Answer 7

the tallest line here is Df = 5
(DF)^2= 25
and
(DE)^2+(EF)^2= \[(2\sqrt{5})^{2} + (\sqrt{5}) ^{2} = 25 \]

Answer 8

that means we have a right angle triangle

Answer 9

this is another way of how to work a problem like that
http://www.teacherschoice.com.au/maths_library/trigonometry/triangle_given_3_points.htm