Question

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

J(-2,7) K(7,2) L(-2,-3) M(-11,2)

Answer 1

`\\ \tt\longmapsto JK=√((7+2)^2+(2-7)^2)=√(81+25)=√(106)`

`\\ \tt\longmapsto KL=√((-2-7)^2+(-3-2)^2)=√(81+25)=√(106)`

`\\ \tt\longmapsto LM=√((-11+2)^2+(2+3)^2)=√(106)`

`\\ \tt\longmapsto JM=√((-11+2)^2+(2-7)^2)=√(106)`

Now

`\\ \tt\longmapsto JL=√((-2+2)^2+(-3-7)^2)=√(100)=10`

`\\ \tt\longmapsto KM=√((-11-7)^2+(2-2)^2)=18`

As sides are equal and diagonals are unequal it's a Rhombus

Answer 2

• B. Rhombus

Explanation:

Plot the points:

• (-2,7), (7,2), (-2,-3), (-11,2)

Connect them in order and connect the diagonals.

See attached.

We see all sides are equal and the diagonals are perpendicular.

This is therefore rhombus