Much appreciated if you could help. :)

The quadrilateral is a parallelogram because it has one pair of opposite sides that are both congruent and parallel ⇒ 2nd answer

Step-by-step explanation:

The formula of a distance between two points is

The formula of a slope of a line is

∵ L (-4 , -4) and M (-1 , -5)

∴ = -4 and = -1

∴ = -4 and = -5

- Use the formula of the distance to find LM

∵

∴ LM =

∵ J (1 , 2) and K (-2 , 3)

∴ = 1 and = -2

∴ = 2 and = 3

- Use the formula of the distance to find JK

∵

∴ JK =

- ML and JK have equal lengths

∴ LM ≅ JK

Use the formula of the slope to find the slopes of LM and JK

∵

∴

∵

∴

- ML and JK have same slopes

∴ LM // JK

∵ LM and JK are opposite sides in the quadrilateral

∵ LM ≅ JK

∵ ML // Jk

- Two opposite sides in the quadrilateral JKLM are congruent

   and parallel

∴ JKLM is a parallelogram

The quadrilateral is a parallelogram because it has one pair of opposite sides that are both congruent and parallel

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,