Topic 3 Test Study Guide

The translation vector <4,5> is applied to ∆BAT to produce the translated image ∆B’A’T’. Assume ∆BAT has no horizontal or vertical side. What is true, and why?

The translation vector <4,5> is applied to ∆BAT to produce the translated image ∆B’A’T’. Assume ∆BAT has no horizontal or vertical side. What is true, and why?

Lines containing corresponding sides of the triangles are parallel because a translation is a rigid transformation and preserves the shape and size of the figure; therefore, the sides of the triangle are still the same. Lines containing corresponding sides of the triangle would be parallel because the slopes would remain the same, therefore, equal, but since having different y-intercepts they would never touch.

A segment in the coordinate plane has an endpoint with coordinates (1,2) and a midpoint with coordinates (4,3). What are the coordinates of the other endpoint, (x,y)? How can we get this value?

The coordinates of the endpoint are (7,4). We can get this by graphing the points and then, looking at the slope of the endpoint and the midpoint, create a line beyond the midpoint with the same slope. This will be the endpoint of the line segment.

Find the slope of line CD if pt. C (-8,-2) and D (-5,-6)

-4/3

Points T, U, and V are collinear. T (-5,6) and U (-2,4), and V lies on the x-axis. What are the coordinates of point V? How do you get this answer?

The coordinates of point V are (4,0). Because V is on the x-axis, we know it has a y-coordinate of 0. We can calculate the slope of the line with the points given, then set the slope equal either point T or V plugged into the slope equation with V as the second pair, or the first. Solve to get x.

To graph a parallel line to the line of the slope a/b, the slope would need to be

a/b

To graph a perpendicular line to the line of slope a/b, the slope would need to be

-b/a

What is the difference between a rigid transformation and a nonrigid transformation?

Rigid transformations preserve the shape and size of a figure, while nonrigid transformations only sometimes preserve shape or size.

Is a rotation rigid or nonrigid?

rigid

Ordered pair rule for rotation 180 degrees about origin

(x,y) → (-x,-y)

Ordered pair rule for rotation 90 degrees clockwise/270 degrees counterclockwise about the origin

(x,y) → (y,-x)

Ordered pair rule for rotation 270 degrees clockwise about origin/90 degrees counterclockwise about the origin

(x,y) → (-y,x)

Is a reflection rigid or nonrigid?

rigid

Rule for reflection across x-axis

(x,y) → (x,-y)

Rule for reflection across y-axis

(x,y) → (-x, y)

Rule for reflection across line y=x

(x,y) → (y,x)

Is a translation rigid or nonrigid?

rigid

Ordered pair notation for translation 5 units up, 2 units right

(x,y) → (x+2, y+5)

Vector notation for a translation

<h,k>

Is a dilation rigid or nonrigid?

nonrigid

Rule for dilation with scale factor 3.5

(x,y) → (3.5x, 3.5y)

dilation, 0 < scale factor < 1, it’s a

reduction

dilation, scale factor = 1, it’s

congruent/no change

dilation, scale factor > 1, it’s a

enlargement

Is a vertical stretch/compression rigid or nonrigid?

nonrigid

Rule for vertical stretch/compression with scale factor 2

(x,y) → (x, 2y)

Is a horizontal stretch/compression rigid or nonrigid?

nonrigid

Rule for horizontal stretch/compression with scale factor 5

(x,y) → (5x, y)