📐 geometry

1. The problem asks for the coordinates of point K' after a reflection across the x-axis. 2. Reflection across the x-axis changes the y-coordinate of a point to its opposite, while

1. **State the problem:** We are given two intersecting lines forming an X shape with four angles labeled 1, 2, 3, and 4. 2. **Given:** $m\angle 3 = 69^\circ$.

1. **State the problem:** We have two similar polygons and need to find the scale factor and the values of $x$, $y$, and $z$. 2. **Given:** Scale factor = 1.67, $x=25$, $y=20$, $z=

1. **State the problem:** We need to solve for $x$ in a right triangle where the hypotenuse is 80 ft, one leg is 48 ft, and the other leg is split into two segments: 30 ft and $x$

1. The problem asks for the formula to find the circumference of a circle given the radius $r = 5$ inches. 2. The formula for the circumference $C$ of a circle using the radius $r$

1. **Stating the problem:** We need to calculate the area of two shapes: a right triangle with legs 3\frac{1}{2} inches and 4 inches, and a trapezoid-like quadrilateral with sides

1. The problem is to show the points, but since no specific points or context are given, we will explain how to represent points in a coordinate system. 2. Points in a 2D plane are

1. **State the problem:** We need to find the surface area of a square-based pyramid with a square base edge of 8.6 cm and four identical isosceles triangular faces, each with a sl

1. **State the problem:** We need to find the surface area of a square-based pyramid where the base is a square with side length 8.6 cm and the triangular faces are identical isosc

1. The problem asks for the radian measure of one of the 12 equal central angles in a circle. 2. The total angle around a point (circle) is $2\pi$ radians.

1. **State the problem:** We are given a circle with a central angle of 70° and the length of the minor arc corresponding to this angle is 7.94 inches. We need to find the circumfe

1. **Stating the problem:** We have triangle HFG with points D on HF and E on HG such that DE is parallel to FG. Given: |DH| = 5 cm, |HE| = 12 cm, |HG| = 30 cm, and the distance fr

1. **State the problem:** We are given two parallel lines $b$ and $c$ cut by a transversal $a$. We know the measures of two angles expressed in terms of $x$: the upper-left angle a

1. **Problem 1: Find the length of segment QV given TQ = 40 units in a diamond-shaped quadrilateral with perpendicular diagonals.** 2. The diagonals of a rhombus (diamond shape) ar

1. **State the problem:** We need to find the area of triangle $\triangle PQR$ where side $r=4$ inches, side $p=8.4$ inches, and the included angle $\angle Q=174^\circ$. 2. **Formu

1. The problem asks to find the area of the given shape. 2. To find the area, we need to know the type of shape and its dimensions.

1. **State the problem:** We need to find the area of a Y-shaped polygon with given side lengths 4.5 m, 12 m, 16 m, 21 m, and 5 m. 2. **Approach:** To find the area of a complex po

1. **State the problem:** Find the area of the given Y-like polygon with a V-shaped notch. 2. **Analyze the shape:** The polygon can be divided into simpler shapes to calculate the

1. **State the problem:** Find the perimeter of the given shape, which consists of a kite-like left section with two equal sides of 20 m each and a right semicircle with diameter 9

1. **Énoncé du problème** : Calculer la distance du point $A(1,2,0)$ au plan $(P)$ d'équation $x + y + z + 1 = 0$. 2. **Formule de la distance d'un point à un plan** :

1. **State the problem:** Find the area of triangle ABC with vertices A(9,9), B(4,-4), and C(-4,1). 2. **Formula used:** The area of a triangle given coordinates $(x_1,y_1)$, $(x_2