Fill In The Blanks[1 Marks ]

Question 11 Mark

AOBC is a rectangle whose three vertices are A(0, – 3), O(0, 0) and B(4, 0). The length of its diagonal is ________.

Answer

AOBC is a rectangle whose three vertices are A(0, - 3), O(0, 0) and B(4, 0). The length of its diagonal is 5 units.
Solution:
$\text{A}(0,3)=(\text{x}_1,\text{y}_1)$
$\text{B}(4,0)=(\text{x}_2,\text{y}_2)$
Now,
$\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(4-0)^2+(0+3)^2}$
$=\sqrt{4^2+3^2}$
$=\sqrt{16+9}$
$=\sqrt{25}$
$=\sqrt{5}\text{unit.}$

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Question 21 Mark

The distance between the points (a, b) and (-a, -b) is _________.

Answer

The distance between the points (a, b) and (-a, -b) is $2\sqrt{\text{a}^2+\text{b}^2}.$
Solution:
Distance between two points $\left( x _1, y _1\right)$ and $\left( x _2, y _2\right)$ can be calculated using the formula
$\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
Therefore, distance between the points (a, b) and (-a,-b) is
$\sqrt{(-\text{a}-\text{a})^2+(-\text{b}-\text{b})^2}$
$\sqrt{4\text{a}^2+4\text{b}^2}$
$2\sqrt{\text{a}^2+\text{b}^2}$

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Question 31 Mark

The distance between the points $\Big(-\frac{8}{5},2\Big)$ and $\Big(\frac{2}{5},2\Big)$is _________.

Answer

The distance between the points $\Big(-\frac{8}{5},2\Big)$ and $\Big(\frac{2}{5},2\Big)$is 2 unit.

Solution: $(\text{x}_1, \text{y}_1)=\Big(-\frac{8}{5},2\Big)$ $ (\text{x}_2, \text{y}_2)=\Big(\frac{2}{5},2\Big)$ $\text{AB}=\sqrt{(\text{x}_1-\text{x}_2)^2+(\text{y}_1-\text{y}_2)^2}$ $\text{AB}=\sqrt{\Big(\frac{2}{5}+\frac{8}{5}\Big)^2+(2-2)}$ $\text{AB}=\sqrt{\Big(\frac{10}{5}\Big)^2+(0)^2}$ $\text{AB}=\sqrt{(2)^2+(0)^2}$ $\text{AB}=\sqrt{4}$ AB = 2 unit

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