Question

figure a was transformed to make figures b, c, and d.
a. which figure is a translation of figure a?
draw an arrow to show the direction of the translation.
b. which figure is a reflection of figure a?
draw the line of reflection.
c. which figure is a rotation of figure a?
is the center of rotation inside, on, or outside the figure?
vocabulary
reflection: a transformation that flips (reflects) a figure across a line to form a mirror image.
rotation: a transformation that turns (rotates) a figure through a given angle and in a given direction around a fixed point.
translation: a transformation that moves (slides) each point of a figure the same distance and in the same direction.

Explanation:

Step1: Identify translation

Translation is moving a figure without rotation or reflection. Figure B is a translation of figure A as it has the same orientation and is just shifted. We can draw an arrow from a point on figure A to the corresponding point on figure B to show the direction of translation.

Step2: Identify reflection

Reflection is flipping a figure across a line to form a mirror - image. Figure D is a reflection of figure A. To draw the line of reflection, we find the mid - points of the line segments connecting corresponding points of figure A and figure D and draw a line perpendicular to these line segments.

Step3: Identify rotation

Rotation is turning a figure around a fixed point. Figure C is a rotation of figure A. To find if the center of rotation is inside, on, or outside the figure, we can try to find the intersection point of the perpendicular bisectors of the line segments connecting corresponding points of figure A and figure C. If this point is inside the figure, the center of rotation is inside; if on the figure, it is on the figure; if outside, it is outside. In this case, the center of rotation is outside the figure.

Answer:

a. Figure B is a translation of figure A. Draw an arrow from a point on figure A to the corresponding point on figure B to show the direction of translation.
b. Figure D is a reflection of figure A. Draw the line of reflection by finding the mid - points of the line segments connecting corresponding points of figure A and figure D and drawing a line perpendicular to these line segments.
c. Figure C is a rotation of figure A. The center of rotation is outside the figure.