📐 geometry

1. **State the problem:** We have trapezoid ABCD with vertices A(-7,5), B(-7,9), C(-3,9), D(-5,1) and its dilation image A'B'C'D' with vertices A'(-2,1), B'(-2,3), C'(0,3), D'(0,-2

1. **State the problem:** We have trapezoid ABCD with vertices A(-6,6), B(-8,8), C(-2,8), D(-6,2) and its dilated image A'B'C'D' with vertices A'(-2,2), B'(-3,3), C'(-1,3), D'(-2,1

1. **State the problem:** We have triangle MNO with vertices M(-6, 9), N(12, 3), and O(3, -12). It is dilated from the origin to triangle M'N'O' with vertices M'(-2, 3), N'(4, 1),

1. **State the problem:** We have parallelogram WXYZ with vertices W(0,0), X(1,2), Y(4,2), Z(3,0). It is dilated from the origin to form W'X'Y'Z' with vertices W'(0,0), X'(2,4), Y'

1. **State the problem:** We have a line segment \(\overline{PQ}\) with endpoints \(P(0,4)\) and \(Q(-6,4)\).

1. **Problem statement:** We are given three points A, B, and C with C due west of B, the bearing of A from B is 241°, and AC = CB. We need to find the bearing of A from C. 2. **Un

1. **State the problem:** We have rectangle DEFG with vertices D(2,4), E(4,7), F(10,3), and G(8,0). We want to find the coordinates of D', E', F', and G' after a dilation with scal

1. **State the problem:** We have a trapezium ABCD with angles at vertices A, B, and D given as $y$, $100^\circ$, and $84^\circ$ respectively. We need to find the value of $y$. 2.

1. **Problem Statement:** We have a square ABCD and its dilated image A'B'C'D' centered at the origin. We need to find the scale factor of the dilation.

1. **State the problem:** We have quadrilateral ABCD with vertices A(3,5), B(5,7), C(8,2), and D(4,-1). It is dilated from the origin to quadrilateral A'B'C'D' with vertices A'(12,

1. **State the problem:** We have triangle $\triangle ABC$ with vertices $A(-2,10)$, $B(4,8)$, and $C(2,4)$. We want to find the coordinates of $A'$, $B'$, and $C'$ after a dilatio

1. **Problem Statement:** We have triangle ABC with vertices A(-2, 10), B(4, 8), and C(2, 4). We need to find the coordinates of A', B', and C' after a dilation with scale factor 3

1. Problem 4.1: In \(\triangle DEF\), \(\angle E = 90^\circ\), \(DE = 15\) m, and \(DF = 17\) m. Find the length of \(EF\). 2. Use the Pythagorean theorem for right triangles: $$DF

1. **Problem Statement:** We have a cube whose side length increases by 10%. We need to find:

1. Let's start by stating the problem: We want to understand what area means in mathematics and how to calculate it. 2. Area is the measure of the amount of space inside a two-dime

1. **Problem Statement:** Calculate the area of the irregular polygon with given side lengths 6 ft, 3 ft, 8 ft, 9 ft, 6 ft, 13 ft, 6 ft, and 8 ft. 2. **Approach:** To find the area

1. **State the problem:** Find the area of the irregular polygon shaped like an arrow using the given side lengths. 2. **Approach:** The polygon can be divided into three rectangle

1. **Problem Statement:** Find the area of the irregular polygon with given side lengths: 15 mm (left vertical), 9 mm (bottom horizontal), 6 mm (right vertical), and smaller segmen

1. **State the problem:** Find the area of the irregular polygon composed of rectangles and triangles with given side lengths. 2. **Analyze the figure:** The polygon can be divided

1. **State the problem:** We need to find the area of a compound figure composed of rectangles and a triangle with given side lengths. 2. **Break down the figure:** The figure can

1. The problem asks to identify which pairs of triangles are congruent by ASA (Angle-Side-Angle). 2. ASA congruence means two triangles are congruent if two angles and the included