Point
\[Q'\] is the image of
\[Q(-7,-6)\] under the translation
\[(x,y)\to(x+12,y+8)\].

To find the coordinates of point \( Q' \), we perform the translation on point \( Q(-7, -6) \) using the given translation rule:

\[
(x, y) \to (x + 12, y + 8)
\]

For point \( Q(-7, -6) \):
- The new \( x \)-coordinate: 
\[
x' = -7 + 12 = 5
\]
- The new \( y \)-coordinate: 
\[
y' = -6 + 8 = 2
\]

Thus, the image of point \( Q \) under the translation is:
\[
Q'(5, 2)
\]

Do you want more details or have any questions about this?

Here are 5 related questions to explore:
1. What is the formula for a general translation in the coordinate plane?
2. How would you perform the translation \( (x, y) \to (x - 5, y + 3) \) on point \( P(4, -1) \)?
3. Can you describe the geometric effect of a translation on any shape in the plane?
4. If a point \( A(1, 2) \) is translated by \( (x - 7, y - 9) \), what is the image of \( A \)?
5. How does translation differ from reflection or rotation in terms of coordinate transformations?

**Tip:** A translation shifts every point of a figure or object by the same distance in the same direction without altering the shape or orientation.

Learn how to find the image of point Q(-7, -6) under the translation (x, y) → (x + 12, y + 8). Step-by-step solution provided with calculations for both x and y coordinates. Suitable for Grades 7-9 students studying coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation