Question

Triangle A″B″C″ is formed by a reflection over x = −3 and dilation by a scale factor of 3 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C′?

coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3

Answer 1

Triangle A"B"C' is formed by reflecting and dilating triangle ABC. The equation for the relationship between the two triangles is triangle A"B"C' = triangle ABC * 3.

Step-by-step explanation:

To find the relationship between triangle ABC and triangle A"B"C', we need to consider the reflection and dilation that has occurred. First, let's focus on the reflection over x = -3. The x-coordinate of a point changes sign when reflected over x = -3. So, the x-coordinates of the vertices of triangle ABC will be positive when reflected, resulting in triangle A"B"C'.

Next, the dilation by a scale factor of 3 from the origin stretches the triangle by a factor of 3 in both the x and y directions. So, the distances between the vertices of triangle ABC and triangle A"B"C' will be 3 times greater for triangle A"B"C'.