📐 geometry

1. The problem asks for the coordinates of the reflection of vertex A across the line $x=6$. 2. The formula for reflecting a point $(x,y)$ across a vertical line $x = k$ is:

1. **State the problem:** We are given the vertices of quadrilateral LMNP as L(-1, 7), M(4, 9), N(8, -1), and P(3, -3). We need to classify LMNP as a parallelogram, rectangle, rhom

1. **State the problem:** We need to find the image of triangle \(\triangle STU\) after reflecting it over the line \(y = 4\). 2. **Reflection formula:** When reflecting a point \(

1. **State the problem:** We need to graph the image of triangle $\triangle TUV$ after reflecting it over the x-axis. 2. **Given vertices:**

1. **State the problem:** We need to find the image of triangle \(\triangle STU\) after reflecting it over the vertical line \(x = -3\). 2. **Reflection rule:** When reflecting a p

1. **State the problem:** We need to find the image of triangle \(\triangle EFG\) after reflecting it over the line \(y=1\). The vertices are \(E(0,5)\), \(F(1,5)\), and \(G(1,3)\)

1. **State the problem:** We need to find the image of triangle \(\triangle QRS\) after reflecting it over the vertical line \(x = -3\). 2. **Recall the reflection rule:** When ref

1. **State the problem:** We need to find the image of trapezoid DEFG after translating it 8 units left and 11 units down. 2. **Recall the translation formula:** For a point $(x,y)

1. **State the problem:** Find the volume of the composite solid consisting of a cone on top of a frustum-like solid. The cone has height $8$ in, the frustum has height $10$ in, th

1. **State the problem:** Find the area of the irregular polygon with given side lengths 6 cm, 2 cm, 8 cm, 3 cm, 5 cm, 2 cm, 2 cm, and 8 cm. 2. **Analyze the figure:** The shape ca

1. **State the problem:** Find the area of the irregular polygon with given side lengths. 2. **Approach:** We can divide the polygon into rectangles and right triangles, calculate

1. **Problem (a):** The area of the square is 100 cm². Find the area of the circle in terms of $\pi$. 2. The square is inscribed in the circle, so the diagonal of the square equals

1. **Problem (a):** Find the volume of a solid cylinder with height and diameter both 9 cm. 2. **Formula:** The volume of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the

1. **Problem statement:** Find the volumes of the given 3D shapes to 1 decimal place. 2. **Formulas:**

1. **Stating the problem:** We are given a 3D shape with an angle $\theta$ at the left-front bottom vertex formed between a slanted segment and a vertical dashed line inside the pr

1. **State the problem:** We have a right triangle with hypotenuse 14, one leg 6, and the other leg $x$ unknown. We need to find the correct formula to calculate $x$. 2. **Recall t

1. **State the problem:** We are given triangle PNO with points Q on PN and R on PO such that QR is parallel to NO. Given lengths are RO = 12.7, PQ = 11.5, and PR = 15.3. We need t

1. **State the problem:** We are given a triangle with vertices F, D, and E. Points G and H lie on sides FD and FE respectively, with segment GH parallel to base DE. Given lengths

1. **State the problem:** We need to find the size of angle $t$ in a quadrilateral where two angles are given as $144^\circ$ and $164^\circ$, and the figure has two parallel sides.

1. **State the problem:** We need to find the length $x$ in a triangle where one angle is $55^\circ$, the adjacent side to this angle is 4 cm, and the opposite side to the angle is

1. **State the problem:** We have a right triangle with one leg measuring 4 cm, an angle of 45°, and the other leg labeled as $x$. We need to find the value of $x$. 2. **Identify t