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Chapter 1: Problem 43

Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane. Original coordinates of vertices: \((-7,-2),(-2,2)\) \((-2,-4),(-7,-4)\) Shift: eight units up, four units to the right

Short Answer

Expert verified
The translated coordinates of the vertices are (-3, 6), (2, 10), (2, 4), (-3, 4).

Step by step solution

01

Understand Translation in Geometry

A translation means shifting a shape in a plane without any rotation or reflection. It requires that every point of the object must move: the same distance and in the same direction. In the context of points on a plane, adding a certain value moves a point right (positive) or left (negative) on the x-axis, and adding a certain value moves a point up (positive) or down (negative) on the y-axis.
02

Identify the Given Original Points and Shift

The given original coordinates of the vertices are (-7,-2),(-2,2),(-2,-4),(-7,-4). The shift applied is eight units up (positive direction along the y-axis), and four units to the right (positive direction along the x-axis).
03

Apply the Shift to the Original Points

For each original point, the shift is applied by adding the shift values to the co-ordinates of the respective vertices. In this case, add 4 to the x-coordinate (for the right shift) and 8 to the y-coordinate (for the upward shift). Hence, the new coordinates are calculated as follows: \[(-7+4,-2+8) = (-3, 6)\] \[(-2+4,2+8) = (2, 10)\] \[(-2+4,-4+8) = (2, 4)\] \[(-7+4,-4+8) = (-3, 4)\]

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