Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
$A(1,-2)$, $B(3,6)$, $C(5,10)$ are three vertices of a parallelogram $ABCD$. Find the fourth vertex $D$.
Step-by-Step Solution
Key Concept: Use the fact that diagonals AC and BD of a parallelogram bisect each other.
Midpoint of $AC=\left(\dfrac{1+5}{2},\dfrac{-2+10}{2}\right)=(3,4)$. [1.0 Mark]
This must also be the midpoint of $BD$: $D_x=2(3)-3=3$; $D_y=2(4)-6=2$. [1.5 Marks]
So $D=(3,2)$. [0.5 Mark]
Correct Answer:
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