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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

1. Translations

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Exercise 10 Page 178

Compare the x- and y-coordinates for the points P and P'. The difference between the coordinates are the values of the vector in the component form.

⟨-1,2⟩

Practice makes perfect

We are given the a point and its image after a translation. P( -3, 6) → P'( -4, 8) We want to find the component form of the vector that translates P to P'. To do so, we must examine what changes between the x-coordinates and the y-coordinates when going from P to P'. Let's write the coordinates of the image as a sum between the preimage coordinates and one missing number.

x: & -3 + = -4 y: & 6 + = 8 For the x-coordinate, we started at -3 and ended at -4. This means we moved 1 unit left. Therefore, we should subtract 1, or add - 1. x: & -3 + ( -1) = -4 y: & 6 + = 8 For the y-coordinate, we started at 6 and ended at 8. This means that we moved 2 units up. Therefore, we should add 2. x: & -3 - 1 = -4 y: & 6 + 2 = 8 The component form of a vertex is written as ⟨ , ⟩ with the translation values for x and y in the blanks. The component form for the translation from P to P' is ⟨-1,2⟩.

Subchapter links

Communicate Your Answer p.173

Monitoring Progress p.175-177

Exercises p.178-180