📐 geometry

1. **State the problem:** Find the image of the point $(-10, -4)$ after a dilation centered at the origin with a scale factor of $\frac{1}{2}$.\n\n2. **Formula for dilation:** The

1. **State the problem:** We need to find the area of a compound figure composed of a large semicircle on top, a vertical rectangular stem, a right-side rectangular extension, and

1. **State the problem:** We have two similar rectangular prisms. The larger prism has a height of 12 cm and a base edge of 3 cm. The smaller prism has a base edge of 2 cm and an u

1. **Problem Statement:** Construct a circle passing through three points $P$, $Q$, and $R$ that are not collinear. 2. **Key Concept:** A unique circle can be drawn through any thr

1. **State the problem:** Find the volume of a sphere with radius $r = 8$ cm. 2. **Formula:** The volume $V$ of a sphere is given by

1. **Problem Statement:** We have parallelogram ABCD reflected across the x-axis and then rotated 180° clockwise about the origin to form parallelogram EFGH.

1. **State the problem:** We have parallelogram ABCD reflected across the x-axis and then rotated 180° clockwise about the origin to form parallelogram EFGH.

1. The problem asks to find the circumference $C$ of a circle given its diameter $d = 22$ yd. 2. The formula for the circumference of a circle is:

1. **State the problem:** We have a circle with a diameter of 22 yards and need to find the area $A$ of the circle in square yards. 2. **Formula used:** The area of a circle is giv

1. **Problem Statement:** Calculate the total volume of a water tank composed of a cylinder and a cone on top. Given:

1. **State the problem:** A pilot uses triangles to find the angle of elevation $\angle A$ from the ground to her plane. Given the triangle with sides 12 km, 20 km, and 20 km, and

1. **State the problem:** We need to find the value of angle $x$ in a circle where two diameters/chords intersect at the center, creating angles marked 52° and $x$, with two inscri

1. **State the problem:** We need to find the perimeter of triangle ABC with an inscribed circle tangent to all three sides. 2. **Given:**

1. **Stating the problem:** Calculate the surface area of a prism with a given base. 2. **Formula:** The surface area $S$ of a prism is given by:

1. **State the problem:** We have two intersecting lines forming vertical and adjacent angles with measures \( (13x + 52)^\circ \), \( z^\circ \), and \( (7x + 82)^\circ \). We nee

1. **Énoncé du problème :** Construire les figures 2, 3, 4 et 5 à partir de la figure 1 en appliquant respectivement :

1. The problem asks to identify which postulates or theorems the LA theorem is a special case of. 2. The LA theorem (Leg Angle theorem) relates to triangle congruence criteria.

1. **Problem Statement:** Hunter drew two identical trapezoids and composed them to form a parallelogram. We need to find the area of one trapezoid using the area of the parallelog

1. **State the problem:** Find the area of the trapezoid with top base 7 m, height 6 m, and bottom base composed of two segments 5 m and 2 m. 2. **Formula for the area of a trapezo

1. **State the problem:** We need to find the distance across the parallelogram-shaped tabletop, which corresponds to the length of the dashed vertical height $h$. 2. **Recall the

1. **State the problem:** We are given points V(-5, -1), W(-6, -3), T(-5, -5), and U(0, -3) and asked to find their coordinates after reflecting them over the y-axis. 2. **Formula