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Three of the vertices of a trapezoid are A(3,-3), B(12, 6) and C(4, 8). The fourth vertex is labeled D. One of its bases is AB.

What is the equation of the line that includes base CD?

A. y = 4x + 1
B. y = 4
C. y = x - 4
D. y = x + 4

Respuesta :

Answer:

Option D

Step-by-step explanation:

Given that three of the vertices of a trapezoid are A(3,-3), B(12, 6) and C(4, 8).

Since AB is the base, we get DC parallel to AB.

In other words, AB and DC will hae the same slope.

To find slope of AB:

Slope of AB =[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{6+3}{9} \\=1[/tex]

Now we have slope of CD as 1, and point as C(4,8)

Use point slope formula to find CD

[tex]y-y_1 = m(x-x_1)y-8=1(x-4)y =x+4[/tex]

Hence option D is right answer

lublana

Answer:

D [tex]y=x+4[/tex]

Step-by-step explanation:

We are given that three vertices of a trapezoid are A(3,-3), B(12,6) and C(4,8).

We have to find the equation of line CD.

Slope formula : [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of AB=[tex]\frac{6+3}{12-3}=1[/tex]

AB is a base of trapezoid.

In trapezoid , one pair of sides are parallel.

In given trapezoid , CD is parallel to AB.

When two lines are parallel then, slopes of lines are equal.

Therefore , slope of CD=1

The equation of line with slope 1 and passing through the point C (4,8) is given by

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values then we get

The equation of line with slope 1 and passing through the point C (4,8) is given by

[tex]y-8=1(x-4)=x-4[/tex]

[tex]y=x-4+8=x+4[/tex]

The equation of line with slope 1 and passing through the point C (4,8) is given by

[tex]y=x+4[/tex]

Answer:D [tex]y=x+4[/tex]

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