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MODEL PAPER 2 (BASIC) — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMODEL PAPER 2 (BASIC)4 Marks
Question
Read the following text carefully and answer the questions that follow:
Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is.
The left-right $($horizontal$)$ direction is commonly called $X-$ axis.
The up $-$ down $($vertical$)$ direction is commonly called $Y-$ axis.
In Green Park, New Delhi Suresh is having a rectangular plot $\text{ABCD}$ as shown in the following figure. Sapling of Gulmohar is planted on the boundary at a distance of $1 m$ from each other. In the plot, Suresh builds his house in the rectangular area $\text{PQRS}$. In the remaining part of plot, Suresh wants to plant grass.
Image
$i$. Find the coordinates of the midpoints of the diagonal $QS$
$ii$. Find the length and breadth of rectangle $\text{PQRS}$?
$iii$. Find Area of rectangle $\text{PQRS}$.
OR
Find the diagonal of rectangle.
✓

Answer

$i.$  Image
Middle point of $QS =\left(\frac{10+3}{2}, \frac{6+2}{2}\right)$
$= (6.5, 4)$
$ii. $ Length $= RS. = \sqrt{(10-3)^2+(2-2)^2}$
$RS. =\sqrt{7^2+0}$
$RS. = 7 m$
Breadth $= RQ = \sqrt{(10-10)^2+(2-6)^2}$
$=\sqrt{0+16}$
$=4 m$
$iii$. Area of rectangle $= 1 \times b$
$=7 \times 4$
$=28 m^2$
OR
Diagonal $=\sqrt{l^2+b^2}$
$=\sqrt{7^2+4^2}$
$=\sqrt{49+16}$
$=\sqrt{65}$

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