AOBC is a rectangle whose three vertices are $A(0, 2)$, $O(0, 0)$ and $B(4, 0)$. The square of the length of…

Question

AOBC is a rectangle whose three vertices are $A(0, 2)$, $O(0, 0)$ and $B(4, 0)$. The square of the length of its diagonal is equal to:

Accepted Answer

## Model Answer The fourth vertex C of rectangle AOBC is at (4, 2). Diagonal = AC (or OB). $OB^2 = (4-0)^2 + (0-0)^2 = 16$ — but OB is a side, not diagonal. Diagonal = AB: $AB^2 = (4-0)^2 + (0-2)^2 = 16 + 4 = \mathbf{20}$ **Answer: B) 20** ## Explanation In rectangle AOBC with A(0,2), O(0,0), B(4,0), the diagonal is the line segment from A(0,2) to B(4,0) (or equivalently from O to C). Using the distance formula: $AB^2 = (4-0)^2 + (0-2)^2 = 16+4 = 20$. Students often mistakenly calculate a side instead of the diagonal — make sure to identify the correct pair of opposite vertices.

Mathematics — Standard (041) — CBSE Class 10 board question