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Coordinate Plane Dilations: Graphing & Understanding

Learn how to graph dilations on a coordinate plane. Understand scale factor and vertices. Practice plotting and connecting dots accurately. Discover how dilation affects shapes. Improve your math skills with practical examples.

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Coordinate Plane Dilations: Graphing & Understanding

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  1. Transparency 8 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 8-3c Objective Graph dilations on a coordinate plane (Get coordinate grid paper for class)

  4. Example 8-3c Vocabulary Dilation An image produced by enlarging or reducing a figure

  5. Lesson 8 Contents Example 1Graph a Dilation Example 2Find and Classify a Scale Factor Example 3Use a Scale Factor

  6. Graph MNO with vertices M(3, –1), N(2, –2), andO(0, 4). Then graph its image M'N'O' after a dilation with a scale factor of . Example 8-1a Plot the coordinates Label each coordinate Connect the dots to make MNO O(0, 4) M(3, -1) N(2, -2) 1/3

  7. Graph MNO with vertices M(3, –1), N(2, –2), andO(0, 4). Then graph its image M'N'O' after a dilation with a scale factor of . Example 8-1a Multiply each number in the ordered pairs by the scale factor O(0, 4) M(3, -1) N(2, -2) 1/3

  8. Example 8-1b M(3, –1) N(2, –2) O(0, 4) 1/3

  9. Graph MNO with vertices M(3, –1), N(2, –2), andO(0, 4). Then graph its image M'N'O' after a dilation with a scale factor of . Example 8-1a Plot the dilation image O’ Label dilation M’ O(0, 4) M(3, -1) N(2, -2) M’ Connect the dots to make M’N’O’ N’ 1/3

  10. Graph MNO with vertices M(3, –1), N(2, –2), andO(0, 4). Then graph its image M'N'O' after a dilation with a scale factor of . Example 8-1a Lay a straight edge from the origin, to the original, to the dilation O’ If all the lines are on the plotted vertices and the origin, then they are plotted correctly O(0, 4) M(3, -1) N(2, -2) M’ Answer: N’ 1/3

  11. Graph JKL with vertices J(2, 4), K(4, –6), and L(0, –4). Then graph its image J'K'L'after a dilation with a scale factor of . Example 8-1d Answer: 1/3

  12. In the figure, segment is a dilation of segment XY. Find the scale factor of the dilation, and classify it as an enlargement or as a reduction. Example 8-2a Make a ratio Choose a point and its dilation 2/3

  13. In the figure, segment is a dilation of segment XY. Find the scale factor of the dilation, and classify it as an enlargement or as a reduction. Example 8-2a y-coordinate of dilation (x’) y-coordinate of original (x) Put the y-coordinate of the dilation (x’) in the numerator Put the y-coordinate of the original (x) in the denominator 2/3

  14. In the figure, segment is a dilation of segment XY. Find the scale factor of the dilation, and classify it as an enlargement or as a reduction. Example 8-2a y-coordinate of dilation (x’) y-coordinate of original (x) 1 Scale factor = 2 The y-coordinate of the dilation is The y-coordinate of the dilation is 1 The y-coordinate of the original is The y-coordinate of the original is 2 2/3

  15. In the figure, segment is a dilation of segment XY. Find the scale factor of the dilation, and classify it as an enlargement or as a reduction. Example 8-2a y-coordinate of dilation (x’) y-coordinate of original (x) Answer: 1 Scale factor = 2 Reduction 1 Since is less than 1 it is a reduction 2 2/3

  16. In the figure, segment is a dilation of segment AB. Find the scale factor of the dilation, and classify it as an enlargement or as a reduction. Example 8-2b Answer: 2; enlargement 2/3

  17. EYES The pupil of Josh’s eye is 6 millimeters in diameter. His eye doctor uses medicine to dilate his pupils by a factor of . Find the new diameter once his pupil is dilated. Example 8-3a Find the new diameter once his pupil is dilated. Write a ratio of dilated eyes to normal eyes dilated eye Define variable normal eye Use the scale factor as the 2nd ratio in the proportion 3/3

  18. EYES The pupil of Josh’s eye is 6 millimeters in diameter. His eye doctor uses medicine to dilate his pupils by a factor of . Find the new diameter once his pupil is dilated. Example 8-3a Cross multiply Bring down 2x = Multiply 6  3 2x 2x = 2x = 6(3) 2x = 2x = 18 3/3

  19. EYES The pupil of Josh’s eye is 6 millimeters in diameter. His eye doctor uses medicine to dilate his pupils by a factor of . Find the new diameter once his pupil is dilated. Example 8-3a Ask “what is being done to the variable?” 2x = 18 The variable is being multiplied by 2 Do the inverse on both sides of the equal sign 3/3

  20. EYES The pupil of Josh’s eye is 6 millimeters in diameter. His eye doctor uses medicine to dilate his pupils by a factor of . Find the new diameter once his pupil is dilated. Example 8-3a Bring down 2x = 18 Using the fraction bar, divide both sides by 2 2x = 18 2x = 18 Combine “like” terms 2 2 Bring down = 1  x 1  x = 9 1  x = Combine “like” terms 3/3

  21. EYES The pupil of Josh’s eye is 6 millimeters in diameter. His eye doctor uses medicine to dilate his pupils by a factor of . Find the new diameter once his pupil is dilated. Example 8-3a Use the Identity Property to multiply 1  x 2x = 18 Bring down = 9 2x = 18 2 2 Add dimensional analysis 1  x = 9 x x = 9 x = 9 mm Answer: The pupil is 9 millimeters in diameter once dilated 3/3

  22. EYES The pupil of Laden’s eye is 8 millimeters in diameter. Her eye doctor uses medicine to dilate her pupils by a factor of . Find the new diameter once her pupil is dilated. Example 8-3c * Answer: 12 mm 3/3

  23. End of Lesson 8 Assignment

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