Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to determine a series of transformations that would map Figure M onto Figure N. ...
TransformationsReflectionsTranslationsCoordinate GeometryGeometric Transformations
2025/5/11
The problem requires us to determine a sequence of transformations that maps Figure M onto Figure N....
TransformationsReflectionTranslationCoordinate Geometry
2025/5/11
The problem presents a partial proof related to a parallelogram. We need to fill in the missing just...
ParallelogramAnglesAlternate Interior AnglesSupplementary AnglesGeometric Proof
2025/5/11
In triangle $OAB$, let $M$ be the midpoint of side $OA$, and let $N$ be the point that divides side ...
VectorsLinear CombinationTriangleIntersection
2025/5/11
Given two points $A(\vec{a})$ and $B(\vec{b})$, we want to find the position vectors of the points t...
VectorsLine SegmentsInternal DivisionExternal Division
2025/5/11
The problem asks us to find the area of a triangle given the coordinates of its vertices. (1) The ve...
AreaTriangleCoordinate Geometry
2025/5/11
Given the magnitudes of vectors $\vec{a}$ and $\vec{b}$ as $|\vec{a}| = 1$ and $|\vec{b}| = 3$, and ...
VectorsDot ProductVector MagnitudeGeometric Algebra
2025/5/11
Find a vector $\vec{b}$ that is perpendicular to the vector $\vec{a} = (1, 3)$ and has a magnitude o...
VectorsDot ProductMagnitudePerpendicularity
2025/5/11
The problem asks to find the angle $\theta$ between two vectors $\vec{a}$ and $\vec{b}$ for three di...
VectorsDot ProductAngle between VectorsTrigonometry
2025/5/11
The problem asks us to find the dot product $\vec{a} \cdot \vec{b}$ of two vectors $\vec{a}$ and $\v...
VectorsDot ProductLinear Algebra
2025/5/11