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MATHEMATICS [2 Mark Question Answer]

Co-ordinate Geometry · ICSE STD 9 (ICSE - English Medium). 21 questions.

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[2 Mark Question Answer]

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21 questions · timed · auto-graded

Question 12 Marks
Find the equation of the line whose $:$ slope $= 0 $ and $y-$intercept $= 0$
Answer
Given
Slope is $0,$ therefore $m = 0$
$Y-$intercept is $0,$ therefore $c = 0$
Therefore,
$y = mx + c$
$y = 0 · x + 0$
$y = 0$
Therefore the equation of the required line is $y = 0$
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Question 22 Marks
Find the equation of the line whose$:$ slope $= 0$ and $y-$ intercept $= - 5$
Answer
Given
Slope is $0,$ therefore $m = 0$
$Y-$intercept is $ - 5,$ therefore $c = - 5$
Therefore,
$y = mx + c$
$y = 0 · x + (- 5)$
$y = - 5$
Therefore the equation of the required line is $ y = - 5$
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Question 32 Marks
Find the equation of the line whose$:$slope$ = - 3 $ and $y-$intercept $= - 1$
Answer
Given
Slope is $- 3,$ therefore $m = - 3$
$Y-i$ntercept is $- 1,$ therefore $c = - 1$
Therefore,
$y = mx + c$
$y = - 3x - 1$
Therefore the equation of the required line is $y = - 3x - 1$
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Question 42 Marks
Find the equation of the line whose$:$slope $= - 4$ and $y-$intercept $= 2$
Answer
Given
Slope is$ - 4,$ therefore $m = - 4$
$Y-$intercept is $2,$ therefore $c = 2$
Therefore,
$y = mx + c$
$y = - 4x + 2$
Therefore the equation of the required line is $y = - 4x + 2$
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Question 52 Marks
Find the equation of the line whose$:$Slope $= 5$ and $y-$intercept $= - 8$
Answer
Given
Slope is $5,$ therefore $m = 5$
$Y-$intercept is $- 8,$ therefore $c = - 8$
Therefore,
$y = mx + c$
$y = 5x + - 8$
Therefore the equation of the required line is $y = 5x + (- 8)$
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Question 62 Marks
Find the equation of the line whose$:$Slope $= 2$ and $y-$intercept $= 3$
Answer
Given
Slope is $2,$ therefore $m = 2$
$Y-i$ntercept is $3,$ therefore $c = 3$
Therefore,
$y = mx + c$
$y = 2x + 3$
Therefore the equation of the required line is $y = 2x + 3$
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Question 72 Marks
For the equation given below, find the slope and the $y-$intercept$:y = 7x - 2$
Answer
Equation of any straight line in the form $y = mx + c,$ where slope $= m($co$-$efficient of $x)$ and $y-$intercept $= c($constant term$)$
$y = 7x - 2$
$y = 7x - 2$
$y = 7x + (- 2)$
Therefore,
slope $=$ co$-$efficient of $x = 7$
$y-$intercept $=$ constant term $= - 2$
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Question 82 Marks
For the equation given below, find the slope and the $y-$intercept$:3x - y - 8 = 0$
Answer
Equation of any straight line in the form $y = mx + c,$ where slope $= m($co$-$efficient of $x)$ and $y-$intercept $= c($constant term$)$
$3x - y - 8 = 0$
$3x - y - 8 = 0$
$- y = - 3x + 8$
$y = 3x + (- 8)$
Therefore,
slope $=$ co$-$efficient of $x = 3$
$y-$intercept $=$ constant term $= - 8.$
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Question 92 Marks
Find the inclination of the line whose slope is$: \frac{1}{\sqrt{3}}$
Answer
If $\tan \theta $ is the slope of a line; then inclination of the line is $\tan \theta $
Here the slope of line is $\frac{1}{\sqrt{3}};$ then $\tan \theta = \frac{1}{\sqrt{3}}$
Now
$\tan \theta = \frac{1}{\sqrt{3}}$
$\tan \theta = \tan 30^\circ $
$\theta = 30^\circ $
Therefore the inclination of the given line is $\theta = 30^\circ $
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Question 102 Marks
Find the inclination of the line whose slope is$: \sqrt{3}$
Answer
If $\tan \theta $ is the slope of a line$;$ then the inclination of the line is $\tan \theta $
Here the slope of line is $\sqrt{3};$ then $\tan \theta = \sqrt{3}$
Now
$\tan \theta = \sqrt{3}$
$\tan \theta = \tan 60^\circ $
$\theta = 60^\circ $
Therefore the inclination of the given line is $\theta = 60^\circ $
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Question 112 Marks
Find the inclination of the line whose slope is$: 1$
Answer
If $\tan \theta $ is the slope of a line$;$ then the inclination of the line is $\tan \theta $
Here the slope of the line is $1;$ then $\tan \theta = 1$
Now
$\tan \theta = 1$
$\tan \theta = \tan 45^\circ $
$\theta = 45^\circ$
Therefore the inclination of the given line is $\theta = 45^\circ .$
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Question 122 Marks
Find the inclination of the line whose slope is$: 0$
Answer
If $\tan \theta $ is the slope of a line$;$ then inclination of the line is $\theta $
Here the slope of line is $0;$ then $\tan \theta = 0$
Now
$\tan \theta = 0$
$\tan \theta = \tan 0^\circ $
$\theta = 0^\circ $
Therefore the inclination of the given line is $\theta = 0^\circ $
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Question 132 Marks
Write the slope of the line whose inclination is$: 60^\circ $
Answer
If $\theta $ is the inclination of a line; the slope of the line is $\tan \theta $ and is usually denoted by letter $m$.
Here the inclination of a line is $60^\circ ,$ then $\theta = 60^\circ $
Therefore the slope of the line is $m = \tan 60^\circ = \sqrt{3}$
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Question 142 Marks
Write the slope of the line whose inclination is$: 45^\circ .$
Answer
If $\theta $ is the inclination of a line; the slope of the line is $\tan \theta $ and is usually denoted by letter $m.$
Here the inclination of a line is $45^\circ ,$ then $\theta = 45^\circ $
Therefore the slope of the line is $m = \tan 45^\circ = 1$
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Question 152 Marks
Write the slope of the line whose inclination is$: 30^\circ $
Answer
If $\theta $ is the inclination of a line; the slope of the line is $\tan \theta $ and is usually denoted by letter $m.$
Here the inclination of a line is $30^\circ ,$ then $\theta = 30^\circ $
Therefore the slope of the line is $m = \tan \theta = 30^\circ =\frac{1}{\sqrt{3}}$.
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Question 162 Marks
Write the slope of the line whose inclination is$: 0^\circ .$
Answer
If $\theta $ is the inclination of a line; the slope of the line is $\tan \theta $ and is usually denoted by letter $m.$
Here the inclination of a line is $0^\circ ,$ then $\theta =0^\circ $
Therefore the slope of the line is $m = \tan 0^\circ = 0$
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Question 172 Marks
In the following, find the inclination of line $\text{AB}:$
Answer
The angle which a straight line makes with the positive direction of $x-$axis $($measured in anticlockwise direction$)$ is called inclination $o$ the line.
The inclination of a line is usually denoted by $\theta $
The inclination is $\theta = 30^\circ $
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Question 182 Marks
In the following, find the inclination of line $\text{AB}:$
Answer
The angle which a straight line makes with the positive direction of $x-$axis $($measured in anticlockwise direction$)$ is called inclination $o$ the line.
The inclination of a line is usually denoted by $\theta $
The inclination is $\theta = 135^\circ $
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Question 192 Marks
In the following, find the inclination of line $\text{AB}:$
Answer
The angle which a straight line makes with the positive direction of the $x-$axis $($measured in an anticlockwise direction$)$ is called inclination o the line.
The inclination of a line is usually denoted by $\theta $
The inclination is $\theta = 45^\circ .$
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Question 202 Marks
Find the values of $x$ and $y$ if$:(3x + 1, 2y - 7) = (9, - 9)$
Answer
Two ordered pairs are equal.
$\Rightarrow $Therefore their first components are equal and their second components too are separately equal.
$(3x + 1, 2y - 7) = (9, - 9)$
$3x + 1 = 9$ and $2y - 7 = -9$
$3x = 8$ and $2y = -2$
$x=\frac{8}{3}$ and $y=-1$
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Question 212 Marks
Find the values of $x$ and $y$ if$:(x - 1, y + 3) = (4, 4)$
Answer
Two ordered pairs are equal.
$\Rightarrow $ Therefore their first components are equal and their second components too are separately equal.
$(x - 1, y + 3) = (4, 4)$
$x - 1 = 4$ and $y + 3 = 4$
$x = 5$ and $y = 1$
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[2 Mark Question Answer] - MATHEMATICS STD 9 Questions - Vidyadip