Question

Triangle TVW is dilated according to the rule (see photo) to create the image triangle T'V'W', which is not shown.

What are the coordinates of the endpoints of segment T'V'?

A) T'(-3,6) and V'(0,3)
B) T'(-3,6) and V'(0,1)
C) T'(-1,2) and V'(0,3)
D) T'(-1,2) and V'(0,1)

Answer 1

Answer:

A) T'(-3,6) and V'(0,3)

Step-by-step explanation:

The dilation rule maps every point (x, y) to (3/4x, 3/4y).  This means the x-coordinate and y-coordinate gets multiplied by 3/4.

The coordinates of T are (-4, 8); this means the coordinates of T' will be

(3/4(-4), 3/4(8)) = (-12/4, 24/4) = (-3, 6).

The coordinates of V are (0, 4); this means the coordinates of V' will be

(3/4(0), 3/4(4)) = (0/4, 12/4) = (0, 3).

This means T'V' will have endpoints at (-3, 6) and (0, 3).

Answer 2

The correct option for the coordinates of the endpoints of segment T'V' formed the dilation triangle TVW according the given rule is option A)

The endpoints of segment T'V'  are A) T'(-3, 6) and V'(0, 3)

The reason for arriving at the above coordinate values is presented as follows:

The given parameters are;

The rule for obtaining triangle T'V'W' from TVW is presented as follows;

$\mathbf{D_{0, \, \dfrac{3}{4} } (x, \, y) \rightarrow \left[\dfrac{3}{4} \cdot x, \, \dfrac{3}{4} \cdot y \right]}$

The coordinate of the vertices of triangle TVC are; T(-4, 8), V(0, 4), and W(4, 4)

The required parameters:

The coordinates of the vertices of T'V'W'

Method:

The rule for the dilation is applied to obtain the coordinates of triangle T'V'W' as follows;

The coordinates of triangle T'V'W' are;

The coordinates of T' = ((3/4)×(-4), (3/4)×(8)) = (-3, 6)

The coordinates of V' = ((3/4)×(0), (3/4)×(4)) = (0, 3)

The coordinates of W' = ((3/4)×(4), (3/4)×(4)) = (3, 3)

Therefore;

The endpoints of the segment T'V' are T'(-3, 6) and V'(0, 3)

The correct option for the coordinates of the endpoint of segment T'V' is (A) T'(-3, 6) and V'(0, 3)

Learn more about dilation transformation rules here

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