Question

Triangle XYZ is dilated by a factor of 3 with the center of dilation at the origin to form triangle X′Y′Z′. What are the coordinates of triangle X′Y′Z′? Question 15 options:
A) X′ (0, 9), Y′ (0, 0), Z′ (15, 0)
B) X′ (0, 6), Y′ (0, 0), Z′ (10, 0)
C) X′ (0, 15), Y′, (0, 0), Z′ (5, 0)
D) X′ (0, 6), Y′ (0, 0), Z′ (15, 0)

Answer 1

Answer:

D) X′ (0, 6), Y′ (0, 0), Z′ (15, 0)

Step-by-step explanation:

From the image attached, given that the location of the triangle is at:

X(0, 2). Y(0, 0), Z(5, 0)

Transformation is the movement of a point from its initial position to a new position. A shape is transformed by transforming all the points in the shape. Types of transformations are reflection, rotation, dilation and translation.

A dilation produces the same shape but different size. If the dilation < 1, then it is a reduction but if dilation > 0 then it is an enlargement.

A point A(x, y) which is dilated by a factor of c at the origin has new coordinates at A'(cx, cy).

Since triangle XYZ is dilated by a factor of 3 with the center of dilation at the origin, this represents an enlargement and the new coordinates of the triangle are:

X'(3*0, 3*2) = X'(0, 6)

Y'(3*0, 3*0) = Y'(0, 0)

Z'(3*5, 3*0) = X'(15, 0)