Coordinate Geometry
NCERT Exemplar Ch 07
CBSE_NCERT_EXEMPLAR_CH07
Grade 10
Question:
If $A(1, 2), B(4, 3), C(6, 6)$ and $D(3, 5)$ are the vertices of a parallelogram $ABCD$, then the midpoint of diagonal $AC$ is:
$\left(\dfrac{7}{2}, 4\right)$
$\left(4, \dfrac{7}{2}\right)$
$(5, 4)$
$\left(\dfrac{5}{2}, 3\right)$
Step-by-Step Solution
Key Concept: Diagonals of a parallelogram bisect each other.
Stepwise Solution:
Midpoint of $AC = \left(\dfrac{1 + 6}{2}, \dfrac{2 + 6}{2}\right) = \left(\dfrac{7}{2}, \dfrac{8}{2}\right) = \left(\dfrac{7}{2}, 4\right)$. [1.0 Mark]
Marking Scheme:
• Midpoint of diagonal $AC = (7/2, 4)$: 1.0 Mark
Correct Answer: $\left(\dfrac{7}{2}, 4\right)$
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