Question

Triangle TUV is similar to triangle XYZ. Which of the following statements is true?

Answer 1

The slope of VT is equal to the slope of ZX.

Explanation:

Two triangles are similar if the slopes of corresponding sides are equal.

In triangle TUV, TU is vertical, so the slope is undefined. The side UV is horizontal, so the slope is zero.

Determine the slope of the VT using the slope formula. Point V is at (-7, -3), and point T is at (-4, 0).

slope=y^2-y1/x^2-x1

=0-(-3)/-4-(-7)

=3/3

=1

In triangle XYZ, XY is vertical, so the slope is undefined. The side YZ is horizontal, so the slope is zero.

Determine the slope of the ZX using the slope formula. Point Z is at (0, 4), and point X is at (6, 10).

slope=y^2-y1/x^2-x1

=10-4/6-0

=6/6

=1

Compare the slopes of corresponding sides of the two triangles.

Sides TU and XY have undefined slopes.

Sides UV and YZ have zero slopes.

Sides VT and ZX have slopes of 1.

Therefore, the following statement is true.

The slope of VT is equal to the slope of ZX.

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Answer 2

Option B. The slope of VT is equal to the slope of ZX

Explanation:

we know that

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

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

step 1

Find the slope VT

we have

V(-7,-3),T(-4,0)

substitute in the formula

`m=(0+3)/(-4+7)`

`m=(3)/(3)`

`m_V_T=1`

step 2

Find the slope ZX

we have

Z(0,4),X(6,10)

substitute in the formula

`m=(10-4)/(6-0)`

`m=(6)/(6)`

`m_Z_X=1`

therefore

The slope of VT is equal to the slope of ZX