Geometry Unit Tests - Transformations & Similarity

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Questions and Answers

What transformation takes figure E to figure F?

Translation

If figures G and H are congruent, what transformation connects them?

Rotation

Identify the single transformation that maps figure J to figure K.

Reflection

What transformation is applied to change figure L to figure M?

Rotation Signup and view all the answers

List the coordinates of point A after translating it 5 units left and 2 units down from (–4, 3).

(–9, 1) Signup and view all the answers

Describe a sequence of transformations that shows Polygon A is congruent to Polygon B.

Reflect Polygon A across a line, then translate it. Signup and view all the answers

What are the resulting coordinates of figure ABCD after a 90-degree clockwise rotation around point C?

Specific coordinates depending on the location of AB and C. Signup and view all the answers

Identify a sequence of transformations that does not return a shape to its original position.

Rotate 90 degrees. Signup and view all the answers

How can you determine which graph represents Cost vs.Volume and which represents Calories vs.Volume?

The graph with a linear relationship that increases suggests Cost vs.Volume, while the one with variations that might increase at different rates suggests Calories vs.Volume. Signup and view all the answers

Which quantities are in a proportional relationship?

Cost vs.Volume appears to be in a proportional relationship. Signup and view all the answers

What is the constant of proportionality for Cost vs.Volume if a drink costs $10 for 20 ounces?

$0.50 per ounce. Signup and view all the answers

What is the weight of a triangle if a circle weighs 3 grams and a square weighs 2 grams in a balanced system?

The triangle weighs 6 grams. Signup and view all the answers

If a system of two equations has a solution of (6,2), what could be a possible form of the other equation?

It could be in the form y = mx + b where the point (6,2) should satisfy it. Signup and view all the answers

What is a characteristic of a system of equations that has exactly one solution?

The lines representing the equations intersect at exactly one point. Signup and view all the answers

How will you find when Josiah and Kiri have the same amount of savings using algebra?

Set the equations 100 + 5x = 40 + 10x and solve for x. Signup and view all the answers

After how many weeks will Josiah and Kiri have the same amount of savings?

After 12 weeks. Signup and view all the answers

What is the slope of the line represented by the points (0, 4) and (-15, 4)?

m = 0 Signup and view all the answers

Determine the slope of the line given the points (8, 2) and (4, 9).

m = -rac{7}{4} Signup and view all the answers

Identify a true statement about the highest daily temperatures in Memphis and Phoenix from the graph.

A. The highest temperature in Phoenix was never the same as the highest temperature in Memphis. Signup and view all the answers

What is the equation that relates the total cost, $y$, of a cell phone plan for $x$ months, starting with $200 and a monthly charge of $50?

y = 200 + 50x Signup and view all the answers

For the new cell phone plan costing $100 to start with a monthly charge of $50, how would its graph differ from the original plan's graph?

It will start lower on the y-axis but have the same slope. Signup and view all the answers

After how many weeks will Joe and Steve have the same amount of money saved, given their saving rates?

After 7 weeks. Signup and view all the answers

What points can be given as coordinates for the line represented by the equation $y = rac{x - 2}{2} + 11$?

(2, 11) and (4, 12) Signup and view all the answers

Given a proportional relationship where raspberries cost twice as much as blueberries, how would the graph look?

The graph would be a straight line through the origin with a slope of 2. Signup and view all the answers

What sequence of transformations will take triangle ABCD to triangle A'B'C'D'?

Reflect triangle ABCD over line p, then reflect the result over line p again. Signup and view all the answers

If you translate a shape 1 unit right, then 4 units left, and then 3 units right, what is the net translation?

The net translation is 0 units to the right. Signup and view all the answers

What does the image of quadrilateral PQRS look like after a dilation centered at O with a scale factor of 1.5?

The image P’Q’R’S’ will be larger than PQRS, with all points moved away from O by a factor of 1.5. Signup and view all the answers

Describe the effect of rotating triangle ABCD 120° counterclockwise around point C, then repeating the rotation.

The shape will be rotated to a new position, then will be rotated again to reach a position equivalent to a 240° rotation. Signup and view all the answers

What is the result of rotating triangle ABCD 180° around point P, followed by reflecting triangle A'B'C'D' across the line through A' and D'?

The final figure, after these transformations, will be called A''B''C''D''. Signup and view all the answers

Why might Triangle 1 and Triangle 2 not be similar despite having a 30º angle?

They may not be similar if the corresponding side lengths do not have the same ratios. Signup and view all the answers

How do you determine the slope of a line given its points?

The slope is found using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with coordinates from two points on the line. Signup and view all the answers

State whether the following is true: Dilations of a triangle keep the angle measures the same.

True, dilations maintain the angle measures of the triangle. Signup and view all the answers

What can you conclude if all points in a graph lie on the same line?

The points are collinear, meaning they share a linear relationship. Signup and view all the answers

Determine the relationship between triangles ABC and DEF if they are similar.

The corresponding sides of triangles ABC and DEF are proportional, and their corresponding angles are equal. Signup and view all the answers

How can you determine which polygons are similar to polygon A?

You can circle the polygons that have the same shape and their corresponding angles equal, regardless of size. Signup and view all the answers

If point B’ has coordinates (4,11) after dilation, how can you determine the scale factor of the dilation with center C?

The scale factor can be found by comparing the distances from C to B and C to B’. Signup and view all the answers

What details should be included when describing the sequence of transformations from polygon A to polygon G?

Include the types of transformations (like translations or rotations) and their specific directions or magnitudes. Signup and view all the answers

What happens to a pre-image when dilated with a scale factor of -3?

The pre-image is not only enlarged but also reflected across the center of dilation. Signup and view all the answers

Based on the equations provided, which graphs share the same y-intercept?

Equations $y = 2x + 5$ and $y = \frac{1}{2}x + 5$ share the y-intercept of 5. Signup and view all the answers

What is the form of the equation for a line with an x-intercept of -2 and a y-intercept of 5?

The equation of the line is $y = -\frac{5}{2}x - 5$. Signup and view all the answers

Study Notes

Unit 1 Test - Transformations

Transformations: Changes made to a figure, like moving, resizing, or flipping it.
Translation: Sliding a figure without rotating or flipping it.
Rotation: Turning a figure around a point.
Reflection: Flipping a figure over a line.
Congruent figures: Figures with the same shape and size.

Unit 2 Test - Dilations, Similarity, and Slope

Dilations: Changes in size of a shape, where all dimensions are multiplied by the same scale factor.
Similar figures: Figures with the same shape but not necessarily the same size. Angle measure is the same in similar figures
Slope: The steepness of a line, calculated as the rise over the run.
Proportional relationship: A relationship where the ratio between two quantities is constant. The graph of a proportional relationship is always a straight line passing through the origin (0,0).

Unit 3 Test - Proportional and Linear Relationships

Proportional relationships: Relationships where the ratio between two quantities is constant. The graph is a straight line through the origin.
y-intercept: Where a line crosses the y-axis on a graph.
x-intercept: Where a line crosses the x-axis on a graph
Slope: The steepness of a line on a graph, often described as "rise over run."
Linear relationship: A relationship on a graph that forms a straight line that does not necessarily go through the origin.

Unit 4 Test - Solving Equations and Systems of Equations

Solving equations: Finding the value of a variable that makes the equation true.
Systems of equations: Two or more equations with the same variables. The solution is the point where the graphs of the equations intersect.
Substitution or elimination methods: Methods used to solve systems of equations.

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Description

Test your knowledge on transformations, dilations, and linear relationships in geometry with these unit tests. Each section covers essential concepts such as translation, rotation, reflection, and proportional relationships. Perfect for students looking to reinforce their understanding of geometric principles.