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Yuki888 [10]
3 years ago
15

What is the most precise name for a quadrilateral with the following vertices:

Mathematics
1 answer:
lozanna [386]3 years ago
8 0

Answer:

The most precise name for a quadrilateral ABCD is a parallelogram

Step-by-step explanation:

we have

A(2,3) B(7,2) C(6,-1) D(1,0)

Plot the quadrilateral'

using a graphing tool

The quadrilateral ABCD in the attached figure

Verify the length of the sides

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

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

step 1

Find distance AB

A(2,3) B(7,2)

substitute

d=\sqrt{(2-3)^{2}+(7-2)^{2}}

d=\sqrt{(-1)^{2}+(5)^{2}}

d_A_B=\sqrt{26}\ units

step 2

Find distance BC

B(7,2) C(6,-1)

substitute

d=\sqrt{(-1-2)^{2}+(6-7)^{2}}

d=\sqrt{(-3)^{2}+(-1)^{2}}

d_B_C=\sqrt{10}\ units

step 3

Find distance CD

C(6,-1) D(1,0)

substitute

d=\sqrt{(0+1)^{2}+(1-6)^{2}}

d=\sqrt{(1)^{2}+(-5)^{2}}

d_C_D=\sqrt{26}\ units

step 4

Find distance AD

A(2,3) D(1,0)

substitute

d=\sqrt{(0-3)^{2}+(1-2)^{2}}

d=\sqrt{(-3)^{2}+(-1)^{2}}

d_A_D=\sqrt{10}\ units

step 5

Compare the length sides

AB=CD

BC=AD

Opposite sides are congruent

<em>Verify the slope of the sides</em>

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

m=\frac{y2-y1}{x2-x1}

step 1

Find slope AB

A(2,3) B(7,2)

substitute

m=\frac{2-3}{7-2}

m=\frac{-1}{5}

m_A_B=-\frac{1}{5}

step 2

Find slope BC

B(7,2) C(6,-1)

substitute

m=\frac{-1-2}{6-7}

m=\frac{-3}{-1}

m_B_C=3

step 3

Find slope CD

C(6,-1) D(1,0)

substitute

m=\frac{0+1}{1-6}

m=\frac{1}{-5}

m_C_D=-\frac{1}{5}

step 4

Find slope AD

A(2,3) D(1,0)

substitute

m=\frac{0-3}{1-2}

m=\frac{-3}{-1}

m_A_D=3

step 5

Compare the slopes

m_A_B=m_C_D

m_B_C=m_A_D

The slope of the opposite sides are equal, that means, opposite sides are parallel

The slopes of consecutive sides are not opposite reciprocal, that means, consecutive sides are not perpendicular

therefore

The most precise name for a quadrilateral ABCD is a parallelogram

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We get 45 + x = 4.5/(0.417 - y)

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So putting (1) in (2) we have

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(45y + 2)/y = 4.5(0.417-y)

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(45y + 2)(0.417 - y) = 4.5y

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