Math Problem Statement

Use the graph and the translation (x, y) → (x + 1, y + 5) to answer parts a and b. Enter the image of each vertex as an ordered pair.

Solution

The problem involves applying the translation rule (x,y)(x+1,y+5)(x, y) \to (x + 1, y + 5) to each vertex of the triangle on the graph. Let's work through this step by step.

Coordinates of the original points:

  • A: Looking at the grid, point AA is at (3,0)(-3, 0).
  • B: Point BB is at (1,2)(-1, -2).
  • C: Point CC is at (4,3)(-4, -3).

Applying the translation (x,y)(x+1,y+5)(x, y) \to (x + 1, y + 5):

  • For A: (3+1,0+5)=(2,5)(-3 + 1, 0 + 5) = (-2, 5)
  • For B: (1+1,2+5)=(0,3)(-1 + 1, -2 + 5) = (0, 3)
  • For C: (4+1,3+5)=(3,2)(-4 + 1, -3 + 5) = (-3, 2)

Final coordinates after translation:

  • A=(2,5)A' = (-2, 5)
  • B=(0,3)B' = (0, 3)
  • C=(3,2)C' = (-3, 2)

You can now enter these values into the answer boxes.

Would you like a more detailed explanation of the translation process or help with part b? Here are five related questions:

  1. How do translations affect the orientation of geometric shapes?
  2. Can translations change the size or shape of a figure?
  3. How do we translate a point if the translation rule was (x2,y+3)(x - 2, y + 3)?
  4. What is the difference between translation and reflection in transformations?
  5. How would you translate a figure using vector notation?

Tip: Always ensure you're applying the translation rule correctly to both the xx- and yy-coordinates to avoid errors!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Translations
Coordinate Geometry
Transformations

Formulas

Translation rule: (x, y) → (x + a, y + b)

Theorems

Concept of Translation in Geometry

Suitable Grade Level

Grades 8-10