Grade General Mathematics Term 3 Study Guide Flashcards

Vocabulary and coordinate rules for transformations, geometric formulas for volume, and proportions used in indirect measurement.

Translation

A transformation that shifts a figure by a specific number of units horizontally and vertically, expressed by the coordinate notation $(x \text{ (right/left)}, y \text{ (up/down)})$, such as $(x+2, y-5)$, representing 2 units right and 5 units down.

Reflection across the x-axis

A transformation where a point $(x, y)$ is flipped over the x-axis to become $(x, -y)$.

Reflection across the y-axis

A transformation where a point $(x, y)$ is flipped over the y-axis to become $(-x, y)$, such as point $B(-1, 2)$ becoming $(1, 2)$.

90 Clockwise Rotation

A transformation about the origin that changes the coordinates of a point following the rule $(y, -x)$, for example, turning point $J(5, 7)$ into $(7, -5)$.

180 Clockwise Rotation

A transformation about the origin that changes the coordinates of a point following the rule $(-x, -y)$, effectively rotating the figure halfway around the origin.

270 Clockwise Rotation

A transformation about the origin that changes the coordinates of a point following the rule $(-y, x)$, rotating the figure three-quarters of the way around.

Reduction

A dilation where the scale factor $k$ is between 0 and 1, represented as $0 < k < 1$.

Enlargement

A dilation where the scale factor $k$ is greater than 1, represented as $k > 1$.

Volume of a Cone

The measure of space inside a cone calculated by the formula $V = \frac{1}{3} \times B \times h$, where $B$ is the base area and $h$ is the height.

Volume of a Sphere

The measure of space inside a sphere calculated by the formula $V = \frac{4}{3} \times \text{base radius}^3 \times \text{pi}$, or $V = \frac{4}{3} \times \frac{22}{7} \times r^3$.

Volume of a Hemisphere

The measure of space inside a half-sphere calculated by the formula $V = \frac{2}{3} \times \text{base radius}^3 \times \text{pi}$, or $V = \frac{2}{3} \times \frac{22}{7} \times r^3$.

Indirect Measurement Proportion

A method of finding unknown heights or distances by setting up a ratio such as $\frac{\text{Height}}{\text{Shadow}} = \frac{\text{Height}}{\text{Shadow}}$, for example: $\frac{x}{2.7} = \frac{3}{2.6}$.

Congruent Triangles

Triangles that are identical in shape and size, where corresponding angles and sides match, such as $\text{Triangle } ABC \text{ is congruent to Triangle } DEF$ meaning $\text{Angle } A$ corresponds to $\text{Angle } D$.

Scale Factor (k)

The ratio that describes how much a figure is enlarged or reduced in a dilation; it can be found by comparing an image point to its preimage point, such as a point moving from 4 to 10 having a scale factor of $2.5$.