📐 geometry

1. **State the problem:** We need to find the coordinates of point $C(-3, 2)$ after it is rotated 270° clockwise around the origin.

1. **State the problem:** We need to find the coordinates of the point $R(3, 3)$ after it is rotated 180° clockwise around the origin.

1. **State the problem:** We need to find the coordinates of point $T'$, which is the image of point $T(-1, 2)$ after a 180° clockwise rotation around the origin. 2. **Formula for

1. **State the problem:** We need to find the coordinates of point $Q(4, -3)$ after it is rotated 180° clockwise around the origin. 2. **Formula for rotation:** Rotating a point $(

1. The problem asks for the central angle of the missing puzzle piece that completes a circle and a semicircle. 2. Recall that a full circle has a total central angle of $$360^\cir

1. **Problem statement:** We are given three points: $A=(5,1)$, $B=(-1,1)$, and $C=(1,4)$. We need to find a fourth point $D$ such that $A$, $B$, $C$, and $D$ form the vertices of

1. **Stating the problem:** We have a parallelogram JKLM with points J(3,3), K(4,3), L(4,1), and M(2,1). The figure is translated by the vector $$\begin{pmatrix} -6 \\ 2 \end{pmatr

1. The problem asks to identify which two angles are vertically opposite angles among the angles a, b, c, d, e, f arranged around a point. 2. Vertically opposite angles are pairs o

1. **State the problem:** Given quadrilateral ABCD with midpoints M, N, O, and P on its sides, prove that quadrilateral MNOP formed by connecting these midpoints is a parallelogram

1. **State the problem:** We have two maps showing the same forest. The first map has a scale of 1 : 20 000 and the forest area is 50 cm². The second map shows the forest area as 8

1. **Problem 1:** Find the area occupied on a plan drawn to a scale of 1 : 500 by the Olympic Stadium in Beijing, which is \(\frac{3}{5}\) of 8 (units not specified, assume 8 squar

1. **State the problem:** We have two maps showing the same forest. The first map has a scale of 1 : 20 000 and the forest area is 50 cm². The second map shows the forest area as 8

1. **State the problem:** We have triangle $\triangle OPQ$ with side $p = 9.7$ inches, angle $\angle Q = 93^\circ$, and angle $\angle O = 82^\circ$. We need to find the length of s

1. **State the problem:** We have triangle $\triangle HIJ$ with side $h = 97$ cm opposite angle $H$, angle $H = 144^\circ$, and angle $I = 24^\circ$. We need to find the length of

1. **State the problem:** We have two similar trapezoidal shapes A and B. Shape A has sides: top = 5 cm, bottom = 7 cm, height = 15 cm.

1. **Énoncé du problème** : On considère un parallélépipède rectangle ABCDA'B'C'D'. Il faut démontrer plusieurs relations vectorielles entre les points. 2. **Rappel des propriétés*

1. **State the problem:** You asked why angle $x$ is $90^\circ$ when the triangle is not right-angled.

1. **State the problem:** We have a circle with center O and a triangle ABC inscribed in it. The segment AB is the diameter of the circle.

1. **Problem:** Determine which combinations of sides are Pythagorean triples. 2. **Definition:** A Pythagorean triple consists of three positive integers $a$, $b$, and $c$ such th

1. **Problem statement:** Dr. Acula jogs around a cemetery forming a polygon with the following path: 3.5 km east, 5 km northeast, 5 km northwest, 5 km southwest, and 3.5 km south,

1. **Problem statement:** A surveyor wants to find the distance $d$ across a lake. The given measurements form a right triangle with legs 90 ft and $(75 + d)$ ft, and the hypotenus