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

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

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

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

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

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

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

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

Example 8-1d 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. Answer: 1/3

Example 8-2a 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. 2/3 Make a ratio Choose a point and its dilation

Example 8-2a 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. 2/3 Put the y-coordinate of the dilation (x’) in the numerator y-coordinate of dilation (x’) Put the y-coordinate of the original (x) in the denominator y-coordinate of original (x)

Example 8-2a 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. 2/3 The y-coordinate of the dilation is y-coordinate of dilation (x’) The y-coordinate of the original is y-coordinate of original (x) 1 The y-coordinate of the dilation is 1 The y-coordinate of the original is 2 2 Scale factor =

Example 8-2a 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. 2/3 Since is less than 1 it is a reduction y-coordinate of dilation (x’) y-coordinate of original (x) 1 2 Scale factor = 1 2 Reduction Answer:

Example 8-2b 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. Answer: 2; enlargement 2/3

Example 8-3a 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. Write a ratio of dilated eyes to normal eyes 3/3 dilated eye normal eye his pupil is dilated. Find the new diameter once Define variable Use the scale factor as the 2 nd ratio in the proportion

Example 8-3a 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. 3/3 Cross multiply 2x2x =2x = 6(3) Bring down 2x = 2x = Multiply 6  3 2x = 18

Example 8-3a 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. 3/3 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

Example 8-3a 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. 3/3 Bring down 2x = 18 2x = 18 Using the fraction bar, divide both sides by Combine “like” terms 1  x Bring down = 1  x = 9 Combine “like” terms 1  x =

Example 8-3a 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. 3/3 2x =  x = 9 Use the Identity Property to multiply 1  x x Bring down = 9 x = 9 Add dimensional analysis x = 9 mm Answer: The pupil is 9 millimeters in diameter once dilated

Example 8-3c 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. Answer: 12 mm * 3/3

End of Lesson 8 Assignment Lesson 4:8Dilations All