Question

The point (−3, −2) is a vertex of a triangle. If the triangle is translated 5 units to the left, what is this point in the translated figure? Draw a graph for yourself if needed.(

Answer 1

To translate a point in the Cartesian coordinate system, you adjust the coordinates based on the translation vector. Translating a point 5 units to the left means you will subtract 5 from the x-coordinate of the point.

Given the original point \( (-3, -2) \):

1. The x-coordinate will change from -3 to \(-3 - 5\).
2. The y-coordinate remains unchanged at -2.

Calculating the new coordinates:

- New x-coordinate: \( -3 - 5 = -8 \)
- New y-coordinate: \(-2\)

Therefore, the vertex of the triangle after the translation is \((-8, -2)\).

So, the point \((-3, -2)\) translated 5 units to the left becomes \((-8, -2)\).