Question

what is the most precise name for a quadrilateral ABCD with vertices A(-5,2),B(-3,5), C(4,5) and D(2,2)

Answer 1

The most precise name for a quadrilateral ABCD is a parallelogram

Explanation:

step 1

Draw the figure

we have that

The coordinates of a quadrilateral are

A(-5,2),B(-3,5), C(4,5) and D(2,2)

using a graphing tool

Plot the coordinates to better understand the problem

see the attached figure

step 2

Find the length sides of the quadrilateral

the formula to calculate the distance between two points is equal to

Find the length side AB

A(-5,2),B(-3,5)

substitute in the formula

Find the length side CD

C(4,5), D(2,2)

substitute in the formula

Find the length side AD

A(-5,2), D(2,2)

substitute in the formula

Find the length side BC

B(-3,5), C(4,5)

substitute in the formula

step 3

Find the slope of the length sides of the quadrilateral

The formula to calculate the slope between two points is equal to

Find the slope of the length side AB

A(-5,2),B(-3,5)

substitute in the formula

Find the slope of the length side CD

C(4,5), D(2,2)

substitute in the formula

Find the slope of the length side AD

A(-5,2), D(2,2)

substitute in the formula

----> is a horizontal line

Find the slope of the length side BC

B(-3,5), C(4,5)

substitute in the formula

substitute in the formula

----> is a horizontal line

step 4

Compare the length sides

opposite sides are congruent

step 5

Compare the slopes

Remember that

If the lines are parallel, then their slopes are the same

so

opposite sides are parallel

therefore

The most precise name for a quadrilateral ABCD is a parallelogram

Explanation:

Answer 2

The most precise name for a quadrilateral ABCD is a parallelogram

Explanation:

step 1

Draw the figure

we have that

The coordinates of a quadrilateral are

A(-5,2),B(-3,5), C(4,5) and D(2,2)

using a graphing tool

Plot the coordinates to better understand the problem

see the attached figure

step 2

Find the length sides of the quadrilateral

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the length side AB

A(-5,2),B(-3,5)

substitute in the formula

`d=\sqrt{(5-2)^(2)+(-3+5)^(2)}`

`d=\sqrt{(3)^(2)+(2)^(2)}`

`d_A_B=√(13)\ units`

Find the length side CD

C(4,5), D(2,2)

substitute in the formula

`d=\sqrt{(2-5)^(2)+(2-4)^(2)}`

`d=\sqrt{(-3)^(2)+(-2)^(2)}`

`d_C_D=√(13)\ units`

Find the length side AD

A(-5,2), D(2,2)

substitute in the formula

`d=\sqrt{(2-2)^(2)+(2+5)^(2)}`

`d=\sqrt{(0)^(2)+(7)^(2)}`

`d_A_D=7\ units`

Find the length side BC

B(-3,5), C(4,5)

substitute in the formula

`d=\sqrt{(5-5)^(2)+(4+3)^(2)}`

`d=\sqrt{(0)^(2)+(7)^(2)}`

`d_B_C=7\ units`

step 3

Find the slope of the length sides of the quadrilateral

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

Find the slope of the length side AB

A(-5,2),B(-3,5)

substitute in the formula

`m=(5-2)/(-3+5)`

`m_A_B=(3)/(2)`

Find the slope of the length side CD

C(4,5), D(2,2)

substitute in the formula

`m=(2-5)/(2-4)`

`m_C_D=(3)/(2)`

Find the slope of the length side AD

A(-5,2), D(2,2)

substitute in the formula

`m=(2-2)/(2+5)`

`m_A_D=0` ----> is a horizontal line

Find the slope of the length side BC

B(-3,5), C(4,5)

substitute in the formula

substitute in the formula

`m=(5-5)/(4+3)`

`m_B_C=0` ----> is a horizontal line

step 4

Compare the length sides

`d_A_B=√(13)\ units`

`d_C_D=√(13)\ units`

`d_A_D=7\ units`

`d_B_C=7\ units`

opposite sides are congruent

step 5

Compare the slopes

Remember that

If the lines are parallel, then their slopes are the same

`m_A_B=(3)/(2)`

`m_C_D=(3)/(2)`

`m_A_D=0`

`m_B_C=0`

so

opposite sides are parallel

therefore

The most precise name for a quadrilateral ABCD is a parallelogram