Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
$A(1,2)$, $B(4,3)$, $C(6,7)$ are three vertices of a parallelogram $ABCD$. Find the fourth vertex $D$.
Step-by-Step Solution
Key Concept: In a parallelogram, the diagonals bisect each other, so the midpoints of AC and BD are equal.
Midpoint of $AC=\left(\dfrac{1+6}{2},\dfrac{2+7}{2}\right)=(3.5,4.5)$. [1.0 Mark]
Since this must also be the midpoint of $BD$: $D=(2(3.5)-4,\ 2(4.5)-3)=(3,6)$. [1.0 Mark]
Correct Answer:
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