📐 geometry

1. The problem asks to find the coordinate notation that represents a translation up 1 unit followed by a reflection over the x-axis. 2. Translation up 1 unit means adding 1 to the

1. The problem asks to find the coordinate notation for a translation up 1 unit followed by a reflection over the x-axis. 2. Translation up 1 unit means adding 1 to the y-coordinat

1. **State the problem:** We have a right triangle with angles 30º, 60º, and 90º. The side opposite the 30º angle is given as $9\sqrt{3}$ mm, and we need to find the length $c$ opp

1. **State the problem:** We have a right triangle with angles 45°, 45°, and 90°, and the hypotenuse is given as $6\sqrt{2}$ meters. We need to find the length of side $g$ adjacent

1. **State the problem:** We need to identify which image shows the preimage rotated 270 degrees counterclockwise around the origin. 2. **Recall the rotation rule:** A rotation of

1. **State the problem:** We need to find the coordinates of point A after two transformations: a translation right 6 units followed by a reflection over the y-axis. 2. **Identify

1. **State the problem:** We need to find the size of angle $x$ in a right-angled triangle where the opposite side to $x$ is 8.6 cm and the adjacent side to $x$ is 3.8 cm. 2. **For

1. **Stating the problem:** We have a prism with a cross-sectional shape of a sector of a circle. The sector has radius $r$ cm, central angle $50^\circ$, the prism length is 20 cm,

1. **Problem Statement:** We have a rectangle AUNT with dimensions $AU=6$ cm (width) and $UN=3$ cm (height). Point $J$ lies on the line extended from the bottom edge $NT$ but outsi

1. **Problem statement:** A closed cylindrical oil can must hold a volume of 1 litre (1000 cm³). We want to find the dimensions (radius $r$ and height $h$) that minimize the surfac

1. **Stating the problem:** We have a triangle with sides labeled 15, 12, and a top side divided into segments 10, $y$, and $x$. There is also a segment of length 4 parallel to the

1. **State the problem:** We have two parallel vertical lines \(\ell, m, n\) and two parallel horizontal lines intersecting them, forming segments. The top horizontal line has segm

1. **State the problem:** Find the distance between the points $(6,5)$ and $(7,8)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

1. The problem asks to find the distance between the points $(0.6, 5)$ and $(7, 8)$. 2. We use the distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$: $$d = \sqrt{(x

1. **State the problem:** We have a square with vertices A(-9, -9), B(9, -9), C(9, 6), and D(-9, 6). We want to find the coordinates of these vertices after a dilation centered at

1. **State the problem:** We have a quadrilateral VUST with vertices V(6,10), U(10,10), S(6,6), and T(10,6). We need to dilate this quadrilateral by a scale factor of $\frac{1}{2}$

1. **State the problem:** We need to find the volume of a prism whose cross-section is composed of two rectangles stacked vertically. 2. **Identify the dimensions:** The bottom rec

1. **Problem Statement:** Find the perimeter of a figure composed of two semicircles with radius 2 cm each, adjacent to each other.

1. **State the problem:** We need to find the midpoint of the line segment AB where A is (1, 4) and B is (7, -2). 2. **Formula for midpoint:** The midpoint M of a segment with endp

1. The problem asks to identify which line segment is an altitude of triangle $\triangle CEG$. An altitude in a triangle is a line segment from a vertex perpendicular to the opposi

1. **State the problem:** We need to identify which line segment is a median of triangle $\triangle RTU$. 2. **Recall the definition of a median:** A median of a triangle is a line