Five-Minute Check (over Lesson 2–6)

Then/Now

New Vocabulary

Key Concept: Translations and Reflections

Example 1: Standardized Test Example

Example 2: Reflections on a Coordinate Plane

Over Lesson 2–6

A. (6, 4)

B. (–6, 4)

C. (6, –4)

D. (–6,–4)

Name the ordered pair for point D.

Over Lesson 2–6

A. (9, 4)

B. (–9, 4)

C. (9, –4)

D. (–9, –4)

Name the ordered pair for point G.

Over Lesson 2–6

A. (5, 0)

B. (0, 5)

C. (–5, 0)

D. (0 –5)

Name the ordered pair for point E.

Over Lesson 2–6

A. point F; quadrant IV

B. point F; quadrant III

C. point F; quadrant II

D. point G; quadrant III

Name the point located at (–3, –3). Then name the quadrant in which the point lies.

Over Lesson 2–6

A. point C; quadrant I

B. point C; quadrant II

C. point A; quadrant I

D. point A; quadrant II

Name the point located at (8, 2). Then name the quadrant in which the point lies.

Over Lesson 2–6

A. (positive, positive)

B. (negative, negative)

C. (positive, negative)

D. (negative, positive)

What are the signs of the x- and y-coordinates of a point located in quadrant IV?

You have already graphed points on a coordinate plane. (Lesson 2–6)

• Define and identify transformations.

• Draw translations and reflections on a coordinate plane.

• Transformation – A movement of a geometric figure.

• Image – Every corresponding point on a figure after its transformation.

• Translation – A transformation where a figure is slid from one position to another without being turned. Slide.

• Reflection – A transformation where a figure is flipped over a line. Flip.

• Line of symmetry – Each half of a figure is mirror image of the other half when a line of symmetry is drawn.

Triangle ABC is shown on the coordinate plane. Find the coordinates of the vertices of the image if the triangle is translated 4 units right and 5 units down.

A A'(–7, 2), B'(–5, –5), C'(1, 0)

B A'(1, 12), B'(3, 5), C'(9, 10)

C A'(–7, 12), B'(–5, 5), C'(1, 10)

D A'(1, 2), B'(3, –5), C'(9, 0)

Read the Test Item

This translation can be written as the ordered pair (4, –5). To find the coordinates of the translated image, add 4 to each x-coordinate and add –5 to each y-coordinate.

Solve the Test Item

Answer: The answer is D.

original translation image

A(–3, 7) + (4, –5) A'(1, 2)

B(–1, 0) + (4, –5) B'(3, –5)

C(5, 5) + (4, –5) C'(9, 0)

A. A'(1, 2), B'(–3, –2), C'(0, –3)

B. A'(3, 2), B'(–1, –2), C'(2, –3)

C. A'(1, 8), B'(–3, –4), C'(0, 3)

D. A'(3, 8), B'(–1, –4), C'(2, 3)

A triangle has vertices at A(2, 5), B(–2, 1) and C(1, 0). What are the coordinates of the vertices if the triangle is translated 1 unit left and 3 units down?

Reflections on a Coordinate Plane

The vertices of figure MNOP are M(–8, 6), N(5, 9), O(2, 1), and P(–10, 3). Graph the figure and the image of the figure after a reflection over the y-axis.To find the coordinates of the vertices of the image after a reflection over the y-axis, multiply the x-coordinate by –1 and use the same y-coordinate.

M(–8, 6) M'(8, 6)

N(5, 9) N'(–5, 9)

O(2, 1) O'(–2, 1)

P(–10, 3) P'(10, 3)

sameopposite

Answer:

Reflections on a Coordinate Plane

A. A'(2, 1), B'(–2, –3), C'(–3, 0)

B. A'(1, –2), B'(–3, 2), C'(2, –3)

C. A'(–1, –2), B'(–3, –2), C'(0, 3)

D. A'(–1, 2), B'(–3, –2), C'(0, –3)

A triangle has vertices at A(1, 2), B(3, –2) and C(0, –3). What are the coordinates of the vertices if the triangle is reflected over the y-axis?