Math Problem Statement

a(2,0)b(-1,5)c(4,3) translation along the vector (0,2)

Solution

To perform a translation of the points A(2,0)A(2, 0), B(1,5)B(-1, 5), and C(4,3)C(4, 3) along the vector (0,2)(0, 2), we simply add the vector to each of the points.

The translation vector (0,2)(0, 2) means we add 0 to the x-coordinate and 2 to the y-coordinate of each point.

Let's calculate the new coordinates:

  1. Point A: A(2+0,0+2)=A(2,2)A'(2 + 0, 0 + 2) = A'(2, 2)

  2. Point B: B(1+0,5+2)=B(1,7)B'(-1 + 0, 5 + 2) = B'(-1, 7)

  3. Point C: C(4+0,3+2)=C(4,5)C'(4 + 0, 3 + 2) = C'(4, 5)

Translated points:

  • A(2,2)A'(2, 2)
  • B(1,7)B'(-1, 7)
  • C(4,5)C'(4, 5)

Would you like further details or have any questions?

Here are five related questions:

  1. How do you find the coordinates after a translation along a general vector?
  2. What is the geometric effect of translating along a vector?
  3. How would the result change if the translation vector was (3,1)(-3, 1)?
  4. Can you perform a reflection after a translation?
  5. How do you compose multiple translations?

Tip: When translating points, keep track of both the horizontal and vertical components of the vector for accurate results.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Translations
Coordinate Geometry

Formulas

Translation Formula: (x', y') = (x + a, y + b)

Theorems

Vector Translation

Suitable Grade Level

Grades 6-8