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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

2 Answers

0 votes

Answer:

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

User Jordi Cruzado
by
7.4k points
1 vote

Answer:

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

User James F
by
6.8k points