MathematicsGrade 7en

🔄 Transformations and Congruence

Master geometric transformations and similarity in Grade 7 Mathematics. This quiz focuses on identifying and performing translations, rotations, reflections, and dilations on figures in the coordinate plane. You'll explore how transformations preserve certain properties, compare congruent and similar shapes, and apply scale factors to solve problems. **What you'll learn:** - Identify and perform translations, rotations, reflections, and dilations - Understand which properties are preserved under each transformation - Distinguish between congruent and similar figures - Apply scale factors and ratios to similar shapes - Verify congruence and similarity using coordinates

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Question 1
A triangle with vertices at $A(1, 2)$ , $B(3, 2)$ , and $C(2, 4)$ is translated 3 units right and 2 units down. What are the coordinates of the new vertex $A'$ ?
Question 2
A translation always preserves the size and shape of a figure, making the image congruent to the original.
Question 3
Which transformation involves turning a figure around a fixed point, usually the origin?
Question 4
A rectangle is reflected across the y-axis. If one vertex was at $(2, 3)$ , where will it be after the reflection?
Question 5
Under a dilation with a scale factor of 2, all side lengths of a figure are doubled, but the angles remain the same.
Question 6
Two figures are congruent if and only if:
Question 7
A triangle with side lengths 3 cm, 4 cm, and 5 cm is dilated with a scale factor of $\frac{1}{2}$ . What are the side lengths of the dilated triangle?
Question 8
Which of the following transformations does NOT preserve congruence?
Question 9
Similar figures have the same shape but can have different sizes, and corresponding angles are equal.
Question 10
A quadrilateral has a perimeter of 20 cm. If it is dilated with a scale factor of 3, what is the perimeter of the dilated quadrilateral?
Question 11
If triangle $ABC$ has sides $AB = 6$ cm, $BC = 8$ cm, and $CA = 10$ cm, and triangle $DEF$ is similar to triangle $ABC$ with a scale factor of $\frac{2}{3}$ , what is the length of side $DE$ (corresponding to $AB$ )?
Question 12
A 90-degree rotation about the origin maps the point $(3, 4)$ to the point $(-4, 3)$ .
Question 13
When reflecting a figure across the line $y = x$ , the point $(a, b)$ maps to:
Question 14
Two rectangles are congruent. If one rectangle has dimensions 5 cm × 8 cm, and the other rectangle is enlarged by a scale factor of 2.5, what are the dimensions of the enlarged rectangle?
Question 15
All rotations preserve the distance between two points, making rotations rigid transformations that create congruent figures.
Question 16
Triangle $PQR$ is reflected across a vertical line. Which property is guaranteed to be preserved?