Question

The points M(-1,-6),N(3,-2),O(1,0) and P (-3,-4) form a quadri. Find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral

Answer 1

we have

M(-1,-6),N(3,-2),O(1,0) and P (-3,-4)

Part 1

slope MN

M(-1,-6),N(3,-2)

m=(-2+6)/(3+1)

m=4/4

m=1

Part 2

Length MN

Applying the formula to calculate the distance between two points

`\begin{gathered} d=\sqrt[]{\mleft(-2+6\mright)^2+}\mleft(3+1\mright)^2 \\ MN=\sqrt[]{32} \end{gathered}`

Part 3

slope NO

N(3,-2),O(1,0)

m=(0+2)/(1-3)

m=2/-2

m=-1

Part 4

Length NO

`\begin{gathered} NO=\sqrt[]{\mleft(0+2\mright)^2+}\mleft(1-3\mright)^2 \\ NO=\sqrt[]{8} \end{gathered}`

Part 5

slope OP

O(1,0) and P (-3,-4)

m=(-4-0)/(-3-1)

m=-4/-4

m=1

Part 6

Length OP

`\begin{gathered} OP=\sqrt[]{\mleft(-4-0\mright)^2+\mleft(-3-1\mright)^2} \\ OP=\sqrt[]{32} \end{gathered}`

Part 7

slope PM

P (-3,-4) and M(-1,-6)

m=(-6+4)/(-1+3)

m=-2/2

m=-1

Part 8

Length PM

`\begin{gathered} PM=\sqrt[]{\mleft(-6+4\mright)^2+}\mleft(-1+3\mright)^2 \\ PM=\sqrt[]{8} \end{gathered}`

part 9

Compare the slopes

we have that

MN=OP

NO=PM

that means

sides MN and OP are parallel

sides NO and PM are parallel

so

opposite sides are parallel

consecutive sides are perpendicular (because the slopes are negative reciprocal)

part 10

compare the lengths

MN=OP

NO=PM

that means

opposite sides are congruent

therefore

Quadrilateral MNOP is a rectangle