Question

Decide whether quadrilateral JKLM is a rectangle, a rhombus, or a square. More than one answer may apply!

J(-4,2) K(0,3) L(1,-1) M(-3,-2)

Answer 1

`\\ \tt\longmapsto JK=√((0+4)^2+(3-2)^2)=√(17)`

`\\ \tt\longmapsto KL=√((1-0)^2+(-1-3)^2)=√(17)`

`\\ \tt\longmapsto LM=√((-3-1)^2+(-2+1)^2)=√(17)`

`\\ \tt\longmapsto JM=√((-3+4)^2+(-2-2)^2)=√(17)`

`\\ \tt\longmapsto JL=√((1+4)^2+(-1-2)^2)=√(34)`

• JL^2=JK^2+KL^2

And as sides are equal it's a square.

Answer 2

Square.

Explanation:

given J(-4,2) || K(0,3) || L(1,-1) || M(-3,-2)

given below the visual answer.

OR

you can find the distance of coordinate to coordinate:

Distance of JK

√(-4-0)² + (2-3)²

√17

Distance of KL

√(0-1)²+(3--1)²

√17

Distance of LM

√(1--3)²+(-1--2)²

√17

Distance of MJ

√(-3--4)²+(-2-2)²

√17

All sides are similar of √17 , so its a square.