📐 geometry

1. **State the problem:** We are given original coordinates of points $A(1,1)$, $B(3,1)$, $C(4,3)$, $D(2,5)$, and $E(0,3)$ and a scale factor $k=1.5$. We need to find the new coord

1. **Problem Statement:** We need to find the perimeter of the five-point star shape given two side lengths: $3$ cm (vertical segment) and $3.5$ cm (horizontal segment).

1. **Problem Statement:** We are given a five-point star shape with two labeled side segments: one vertical segment labeled $3$ cm and one horizontal segment labeled $3.5$ cm.

1. **State the problem:** We have an equilateral triangle with one side length $\sqrt{10}$ and a perpendicular segment $x$ from the bottom vertex to the opposite side. We need to f

1. **Problem 16:** Given that $\overrightarrow{PD}$ bisects $\angle BPE$, the two angles formed by the bisector are equal. 2. This means:

1. **Problem 14:** Find $m\angle VUZ$ given $m\angle VUT = 122^\circ$, $m\angle VUZ = 4x + 8$, and $m\angle ZUT = 14x + 6$. 2. **Understanding the problem:** Angles $VUZ$, $ZUT$, a

1. **Problem Statement:** We are given a protractor diagram with rays from point $A$ to points $B$, $C$, $D$, $E$, and $F$. We need to find the measures of angles $m\angle BAC$, $m

1. **State the problem:** We are given that point C lies between points B and D on segment BD.

1. **State the problem:** We need to find the area of a trapezoid with top base $12$ mm, bottom base $9$ mm, and height $5$ mm. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths $38$ ft and $19$ ft, and height $8.5$ ft. 2. **Formula for the area of a trapezoid:**

1. **Problem:** Find the coordinates of point $B$ after a dilation with scale factor $2.5$ centered at the origin. 2. **Rule for dilation from the origin:**

1. **State the problem:** We have a line segment $EF$ that undergoes a dilation centered at the origin with a scale factor of $3$.

1. **State the problem:** Noor needs to dilate the line segment with endpoints $A(1,4)$ and $B(8,-1)$ by a scale factor of $\frac{1}{2}$ about the origin.

1. **State the problem:** We need to find the area of the top of a jelly doughnut, which is a circle with radius $3.5$ inches. 2. **Formula:** The area $A$ of a circle is given by

1. **State the problem:** We need to find an equation to determine the diameter of a circular track given its circumference of $62.8$ meters. 2. **Recall the formula for circumfere

1. **State the problem:** We need to find the circumference of a pizza with a diameter of $8$ inches. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. The problem asks to understand how an irregular polygon was split into 4 similar shapes. 2. Similar shapes have the same shape but may differ in size; they have equal correspond

1. **State the problem:** A helicopter flies $60$ miles west and then $25$ miles north from Redville to Leek. We need to find the straight-line distance from Redville to Leek.

1. **State the problem:** We are given the formula for the area of a circle $$A = \pi r^2$$ and asked to solve for the radius $$r$$. 2. **Formula and rules:** The area $$A$$ of a c

1. **Problem Statement:** We have triangle $XYZ$ with vertices $Z$ at upper-left, $Y$ at lower-left, and $X$ at right. We need to draw three rotations of this triangle around point

1. **State the problem:** We start with point $A$ at coordinates $(3,4)$.