215k views
5 votes
If mnp has vertices at m (-5,-7) , N (7,-2) andcp (2,10) is mnp isoscles?

User Tinazmu
by
8.5k points

2 Answers

4 votes
check the picture below.

now, clearly the longest side is MP, and for a triangle to be an isosceles, it has to have two equal sides, so two sides must be twins.

since MP is the longest one, that only leaves out NP and NM, are they twins?


\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &N&(~ 7 &,& -2~) % (c,d) &P&(~ 2 &,& 10~) \end{array}\\\\\\ % distance value d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ NP=√([2-7]^2+[10-(-2)]^2)\implies NP=√((2-7)^2+(10+2)^2) \\\\\\ NP=√((-5)^2+12^2)\implies NP=√(25+144)\implies \boxed{NP=13}

and now let's check NM


\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &N&(~ 7 &,& -2~) % (c,d) &M&(~ -5 &,& -7~) \end{array}~~~ \\\\\\ NM=√([-5-7]^2+[-7-(-2)]^2)\\\\\\ NM=√((-5-7)^2+(-7+2)^2) \\\\\\ NM=√((-12)^2+(-5)^2)\implies NM=√(144+25)\implies \boxed{NM=13}
If mnp has vertices at m (-5,-7) , N (7,-2) andcp (2,10) is mnp isoscles?-example-1
User Danny Parker
by
7.6k points
0 votes
My graphing program shows two of the side lengths are the same.

ΔMNP IS isosceles.
If mnp has vertices at m (-5,-7) , N (7,-2) andcp (2,10) is mnp isoscles?-example-1
User Gianinna
by
9.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories