Question

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

Answer 1

D
`y=x+4`

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 :
`m=(y_2-y_1)/(x_2-x_1)`

Slope of AB=
`(6+3)/(12-3)=1`

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

`y-y_1=m(x-x_1)`

Substitute the values then we get

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

`y-8=1(x-4)=x-4`

`y=x-4+8=x+4`

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

`y=x+4`

Answer:D
`y=x+4`

Answer 2

Option D

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 =
`(y_2-y_1)/(x_2-x_1)\\=(6+3)/(9) \\=1`

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

Use point slope formula to find CD

`y-y_1 = m(x-x_1)y-8=1(x-4)y =x+4`

Hence option D is right answer