Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Show, using the distance formula, that the points $(1,7)$, $(4,2)$, $(-1,-1)$, $(-4,4)$ are the vertices of a square.
Step-by-Step Solution
Key Concept: Compute all four sides and both diagonals; a square requires all sides equal and both diagonals equal.
$AB=\sqrt{9+25}=\sqrt{34}$; $BC=\sqrt{25+9}=\sqrt{34}$; $CD=\sqrt{9+25}=\sqrt{34}$; $DA=\sqrt{25+9}=\sqrt{34}$. All four sides are equal. [1.5 Marks]
$AC=\sqrt{4+64}=\sqrt{68}$; $BD=\sqrt{64+4}=\sqrt{68}$. Both diagonals are equal. [1.0 Mark]
Since all sides are equal and both diagonals are equal, $ABCD$ is a square. [0.5 Mark]
Correct Answer:
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