1. On the coordinate plane, $$ riangle X Y Z $$ has vertices of $$ X(0,4), Y(2,-1) $$, and $$ Z(-4,2) $$. What are the vertex coordinates of the triangle after a dilation centered at the origin with a scale factor of 5 ? $$ X^{\prime}(0,8), Y^{\prime}(20,-10), Z^{\prime}(-8,4) $$ $$ X^{\prime}(0,12), Y^{\prime}(6,-3), Z^{\prime}(-12,6) $$ $$ X^{\prime}(5,9), Y^{\prime}(7,4), Z^{\prime}(1,7) $$ $$ X^{\prime}(0,20), Y^{\prime}(10,-5), Z^{\prime}(-20,10) $$

Question

1. On the coordinate plane, $$ 	riangle X Y Z $$ has vertices of $$ X(0,4), Y(2,-1) $$, and $$ Z(-4,2) $$. What are the vertex coordinates of the triangle after a dilation centered at the origin with a scale factor of 5 ? $$ X^{\prime}(0,8), Y^{\prime}(20,-10), Z^{\prime}(-8,4) $$ $$ X^{\prime}(0,12), Y^{\prime}(6,-3), Z^{\prime}(-12,6) $$ $$ X^{\prime}(5,9), Y^{\prime}(7,4), Z^{\prime}(1,7) $$ $$ X^{\prime}(0,20), Y^{\prime}(10,-5), Z^{\prime}(-20,10) $$

UpStudy AI · Accepted Answer

To perform a dilation of a point $$(x,y)$$ centered at the origin with a scale factor of $$5$$, we multiply both coordinates by $$5$$. We apply this to each vertex of the triangle.

1. For vertex $$X(0,4)$$:
   $$
   X' = (5 \times 0,\; 5 \times 4) = (0, 20)
   $$

2. For vertex $$Y(2,-1)$$:
   $$
   Y' = (5 \times 2,\; 5 \times -1) = (10, -5)
   $$

3. For vertex $$Z(-4,2)$$:
   $$
   Z' = (5 \times -4,\; 5 \times 2) = (-20, 10)
   $$

Thus, the vertex coordinates of the dilated triangle are:
$$
X'(0,20),\quad Y'(10,-5),\quad Z'(-20,10)
$$

Comparing with the options provided, the correct answer is:

$$ X^{\prime}(0,20),\; Y^{\prime}(10,-5),\; Z^{\prime}(-20,10) $$
The vertex coordinates after dilation are $$ X'(0,20), Y'(10,-5), Z'(-20,10) $$.

On the coordinate plane, has vertices of , and . What are the vertex coordinates of the triangle after a dilation centered at the origin with a scale factor of 5 ?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions