Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

We are given an equilateral triangle with side length 2. $M$ is the midpoint of side $BC$. We need t...

VectorsDot ProductEquilateral TriangleGeometric Proofs

The problem asks to find the dot product of two vectors $\vec{a}$ and $\vec{b}$ given their magnitud...

VectorsDot ProductTrigonometry

Given the coordinates of points $A(-2, 1)$, $B(1, 0)$, and $C(2, 4)$, find the coordinates of point ...

Coordinate GeometryVectorsParallelogramsGeometric Proof

Given points $A(-2, 1)$, $B(1, 0)$, and $C(2, 4)$, find the coordinates of point $D$ such that $ABCD...

GeometryParallelogramCoordinate GeometryMidpoint Formula

The problem asks us to find the vector $AB$ in component form and its magnitude given two points $A$...

Vectors2D VectorsVector ComponentsVector MagnitudeCoordinate Geometry

The problem asks us to express $tan(\theta)$ in terms of $x$, given a right triangle with legs of le...

TrigonometryRight TrianglesPythagorean TheoremTangent Function

Given triangle $OFC$, points $A$ and $B$ are on segment $OC$ such that $A$ is closer to $O$ and $B$ ...

GeometryHomothetyThales' TheoremSimilar TrianglesGeometric Transformations

We are given a geometric transformation $f$ defined by the equations: $x' = y + 1$ $y' = x - 1$ We n...

Geometric TransformationsIsometryGlide ReflectionCoordinate GeometryLinear Transformations

We are given a square $ABCD$ with center $O$ and direct orientation. We are also given some transfor...

TransformationsTranslationAnalytic GeometryCirclesCoordinate Geometry

Let $h_1$ be a homothety with center A and ratio -2. Let $h_2$ be a homothety with center B and rati...

HomothetyTransformationsTranslationsGeometric TransformationsComposition of Transformations

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