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Point P'(1,5) is the image of P(-3, 1) under a translation. Determine the translation. Use non-negative numbers. units to the right/left and units up/down A translation by

Point P'(1,5) is the image of P(-3, 1) under a translation. Determine the translation. Use non-negative numbers. units to the right/left and units up/down A translation by

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Translation Introduction (Example for Educational Website):** **Understanding Translations on a Coordinate Plane** When translating a point on a coordinate plane, each point's location is shifted horizontally, vertically, or both. This process involves moving points a specific number of units to the right or left and/or up or down. **Example Problem** **Given:** Point \( P'(1, 5) \) is the image of \( P(-3, 1) \) under a translation. **Task:** Determine the translation. Use non-negative numbers. **Solution:** To find the translation, observe the changes in the \(x\)-coordinates and \(y\)-coordinates from point \( P \) to point \( P' \). 1. **Horizontal Translation (along the \( x \)-axis):** - The initial \( x \)-coordinate of \( P \) is -3. - The \( x \)-coordinate after translation \( P' \) is 1. - Change in \( x \)-coordinate is \( 1 - (-3) = 1 + 3 = 4 \). - Therefore, the horizontal translation is 4 units to the right. 2. **Vertical Translation (along the \( y \)-axis):** - The initial \( y \)-coordinate of \( P \) is 1. - The \( y \)-coordinate after translation \( P' \) is 5. - Change in \( y \)-coordinate is \( 5 - 1 = 4 \). - Therefore, the vertical translation is 4 units up. So, the translation can be described as a movement of: - 4 units to the right - 4 units up This completes the description of how the point \( P(-3, 1) \) has been translated to point \( P'(1, 5) \). **Final Answer:** A translation by **4 units right** and **4 units up**.
Transcribed Image Text:**Translation Introduction (Example for Educational Website):** **Understanding Translations on a Coordinate Plane** When translating a point on a coordinate plane, each point's location is shifted horizontally, vertically, or both. This process involves moving points a specific number of units to the right or left and/or up or down. **Example Problem** **Given:** Point \( P'(1, 5) \) is the image of \( P(-3, 1) \) under a translation. **Task:** Determine the translation. Use non-negative numbers. **Solution:** To find the translation, observe the changes in the \(x\)-coordinates and \(y\)-coordinates from point \( P \) to point \( P' \). 1. **Horizontal Translation (along the \( x \)-axis):** - The initial \( x \)-coordinate of \( P \) is -3. - The \( x \)-coordinate after translation \( P' \) is 1. - Change in \( x \)-coordinate is \( 1 - (-3) = 1 + 3 = 4 \). - Therefore, the horizontal translation is 4 units to the right. 2. **Vertical Translation (along the \( y \)-axis):** - The initial \( y \)-coordinate of \( P \) is 1. - The \( y \)-coordinate after translation \( P' \) is 5. - Change in \( y \)-coordinate is \( 5 - 1 = 4 \). - Therefore, the vertical translation is 4 units up. So, the translation can be described as a movement of: - 4 units to the right - 4 units up This completes the description of how the point \( P(-3, 1) \) has been translated to point \( P'(1, 5) \). **Final Answer:** A translation by **4 units right** and **4 units up**.
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