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Maths 1 Marks Question

P-2 Co-ordinate Geometry · Maharashtra Board STD 10 (MSBSHSE - Semi English Medium). 16 questions.

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Question 11 Mark
Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.
90°
Answer
slope is given as the tangent of the angle formed with the positive direction of x-axis

3. tan 90° = cannot be determined.

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Question 21 Mark
Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.
60°
Answer
slope is given as the tangent of the angle formed with the positive direction of x-axis2. tan60° = $\sqrt 3$
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Question 31 Mark
Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.
45°
Answer
slope is given as the tangent of the angle formed with the positive direction of x-axis

1. tan 45° = 1

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Question 41 Mark
If slope of the line joining points $\mathrm{P}(\mathrm{k}, 0)$ and $\mathrm{Q}(-3,-2)$ is $\frac{2}{7}$ then find $k$.
Answer
$\mathrm{P}(\mathrm{k}, 0)$ and $\mathrm{Q}(-3,-2)$
Slope of line $\mathrm{PQ}=\frac{-2-0}{-3-k}=\frac{-2}{-3-k}$
But slope of line PQ is given to be $\frac{2}{7}$.
$
\therefore \frac{-2}{-3-k}=\frac{2}{7} \quad \therefore k=4
$
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Question 51 Mark
Show that points $\mathrm{P}(-2,3), \mathrm{Q}(1,2), \mathrm{R}(4,1)$ are collinear.
Answer
$\mathrm{P}(-2,3), \mathrm{Q}(1,2)$ and $\mathrm{R}(4,1)$ are given points
slope of line $\mathrm{PQ}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-3}{1-(-2)}=-\frac{1}{3}$
Slope of line $\mathrm{QR}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{4-1}=-\frac{1}{3}$
Slope of line PQ and line $\mathrm{QR}$ is equal.
But point $Q$ lies on both the lines.
$\therefore$ Point P, Q, R are collinear.
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Question 61 Mark
Find the slope of the line passing through the points $\mathrm{A}(-3,5)$, and $\mathrm{B}(4,-1)$
Answer
Let, $x_1=-3, \quad x_2=4, \quad y_1=5, \quad y_2=-1$
$\therefore$ Slope of line $\mathrm{AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-5}{4-(-3)}=\frac{-6}{7}$
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Question 71 Mark
Find the slope of a line which makes an angle with the positive X -axis.
(i) $0^{\circ}$ (ii) $30^{\circ}$ (iii) $45^{\circ}$ (iv) $60^{\circ}$ (v) $90^{\circ}$
Answer
(i) 0, (ii) $\frac{1}{\sqrt{3}}$, (iii) 1, (iv) $\sqrt{3}$, (v) not defined
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Question 81 Mark
Find the distance between the given points.
(i) A (3,-4), B (-5, 6)
(ii) P (10, -8), Q (-3, -2)
(iii) K (0, -5), L (-5, 0)
(iv) I (3.5, 6.8), J (1.5, 2.8)
Answer
(i) $2 \sqrt{41}$ (ii) $\sqrt{205}$ (iii) $5 \sqrt{2}$ (iv) $2 \sqrt{5}$
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Question 91 Mark
Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.
90°
Answer
slope is given as the tangent of the angle formed with the positive direction of x-axis
tan 90° = cannot be determined.
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Question 111 Mark
Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.
45°
Answer
slope is given as the tangent of the angle formed with the positive direction of x-axis
tan 45° = 1
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Question 121 Mark
Show that points $\mathrm{P}(-2,3), \mathrm{Q}(1,2), \mathrm{R}(4,1)$ are collinear.
Answer
$\mathrm{P}(-2,3), \mathrm{Q}(1,2)$ and $\mathrm{R}(4,1)$ are given points
slope of line $\mathrm{PQ}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-3}{1-(-2)}=-\frac{1}{3}$
Slope of line $\mathrm{QR}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{4-1}=-\frac{1}{3}$
Slope of line PQ and line $\mathrm{QR}$ is equal.
But point $Q$ lies on both the lines.
$\therefore$ Point P, Q, R are collinear.
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Question 131 Mark
If slope of the line joining points $\mathrm{P}(\mathrm{k}, 0)$ and $\mathrm{Q}(-3,-2)$ is $\frac{2}{7}$ then find $k$.
Answer
$\mathrm{P}(\mathrm{k}, 0)$ and $\mathrm{Q}(-3,-2)$
Slope of line $\mathrm{PQ}=\frac{-2-0}{-3-k}=\frac{-2}{-3-k}$
But slope of line PQ is given to be $\frac{2}{7}$.
$\therefore \frac{-2}{-3-k}=\frac{2}{7} \quad \therefore k=4
$
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Question 141 Mark
Find the slope of the line passing through the points $\mathrm{A}(-3,5)$, and $\mathrm{B}(4,-1)$
Answer
Let, $x_1=-3, \quad x_2=4, \quad y_1=5, \quad y_2=-1$
$\therefore$ Slope of line $\mathrm{AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-5}{4-(-3)}=\frac{-6}{7}$
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Question 151 Mark
Find the slope of a line which makes an angle with the positive X -axis.
(i) $0^{\circ}$ (ii) $30^{\circ}$ (iii) $45^{\circ}$ (iv) $60^{\circ}$ (v) $90^{\circ}$
Answer
(i) 0, (ii) $\frac{1}{\sqrt{3}}$, (iii) 1, (iv) $\sqrt{3}$, (v) not defined
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Question 161 Mark
Find the distance between the given points.
(i) A (3,-4), B (-5, 6)
(ii) P (10, -8), Q (-3, -2)
(iii) K (0, -5), L (-5, 0)
(iv) I (3.5, 6.8), J (1.5, 2.8)
Answer
(i) $2 \sqrt{41}$ (ii) $\sqrt{205}$ (iii) $5 \sqrt{2}$ (iv) $2 \sqrt{5}$
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