3 Marks Question

Question 13 Marks

Write the coordinates of each of the points $P, Q, R, S, T$ and $O$ from the:

Answer

Thinking Process:
Firstly, draw the perpendicular lines from the point to the coordinates axes.
Further, measure the distance from intersecting points to the origin along their sign.
Finally, write the $x$ unit distance and $y$ unit distance in pair.
Sol. The coordinates of the points $P, Q, R, S, T$ and $O$ are $P(1, 1), Q(-3, 0), R(-2, -3), S(2, 1), T (4, -2)$ and $O(0, 0).$

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Question 23 Marks

Plot the following points and write the name of the figure obtained by joining them in order: $P(-3, 2), Q(-7, -3), R(6, -3), S(2, 2).$

Answer

Let $X’ OX$ and $Y’ OY$ be the coordinate axes and mark point on it. Here, point $P(-3, 2)$ lies in II quadrant, $Q(-7, -3)$ lies in III quadrant, $R(6, -3)$ lies in $IV$ quadrant and $S(2, 2)$ lies in I quadrant. Plotting the points on the graph paper, the figure obtained is trapezium $PQRS.$

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Question 33 Marks

Plot the points $P(1, 0), Q(4, 0)$ and $S(1, 3)$. Find the coordinates of the point $R$ such that $PQRS$ is a square.

Answer

In point $P(1,0), y$-coordinate is zero, so it lies on $X$-axis. In point $Q(4,0), y$-coordinate is zero so it lies on $X$-axis. In point $S (1,3)$, both coordinates are positive, so it lies in I quadrant. On plotting these points, we get the following graph.

Now, take a point $R$ on the graph such that $PQRS$ is a square. Then, all sides will be equal i.e., $P Q=Q R=R S=P S$. So, abscissa of $R$ should be equal to abscissa of $Q$ i.e., $4$ and ordinate of $R$ should be equal to ordinate of $S$ i.e., 3 . Hence, the coordinates of $R$ are $(4,3)$.

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Question 43 Marks

Taking $0.5\ cm$ as $1$ unit, plot the following points on the graph paper: $A(1, 3), B(-3, -1), C(1, -4), D(-2, 3), E(0, -8), F(1, 0)$

Answer

Here, in point $4(1,3)$ both $x$ and $y$-coordinates are positive, so it lies in $I$ quadrant. In point $8(-3,-1)$, both $x$ and $y$ coordinates are negative, so it lies in $III$ quadrant. In point $C(1,-4), x$-coordinate is positive and $y$-coordinate is negative, so it lies in $IV$ quadrant. In point $D (-2,3)$, $x$-coordinate is negative and $y$-coordinate is positive, so it lies in $II$ quadrant. In point $E(0,-8) x$-coordinate is zero, so it lies on $Y$-axis and in point $F(1,0), y$-coordinate is zero, so it lies on $X -$axis. On plotting the given points, we get the following graph.

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Question 53 Marks

Find the coordinates of the point:
$i.$ Which lies on $x$ and $y$ axes both.
$ii.$ Whose ordinate is $-4$ and which lies on $y-$axis.
$iii.$ whose abscissa is $5$ and which lies on $x-$axis.

Answer

$i.$ The coordinates of the point which lies on both the axes are $(0, 0)$.
$ii.$ The coordinates of the point whose ordinate is $-4$ and which lies on $y-$axis are $(0, -4)$.
$iii.$ The coordinate of the point whose abscissa is $5$ and which lies on $x-$axis are $(5, 0)$.

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Question 63 Marks

Plot the following points and check whether they are collinear or not: $(0, 0), (2, 2), (5, 5)$

Answer

Plotting the points $0 (0, 0), A (2, 2)$ and $6 (5, 5)$on the graph paper and join these points, we get a straight line. Hence, given points are collinear.

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Question 73 Marks

Plot the following points and check whether they are collinear or not:
$(1, 1), (2, -3), (-1, -2)$

Answer

Plotting the points $P (1,1), 0 (2, -3)$ and $R (-1, -2)$ on the graph paper and join these three points, we get three lines i.e., the given points do not lie on the same line. So, given points are not collinear.

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Question 83 Marks

From the answer the following:

$i.$ Write the points whose abscissa is $0$
$ii.$ Write the points whose ordinate is $0$
$iii.$ Write the points whose abscissa is $-5$

Answer

$i.$ Clearly, the distance of points $A, L$ and $O$ from $y$-axis is $0$ .
So, $A(0,3), L(0,-4)$ and $O(0,0)$ are the points whose abscissa is $0 .$
$ii.$ Clearly, the distance of points $G, I$ and $O$ from $x-$axis is $0$ .
So, $G(5,0), I(-2,0)$ and $O(0,0)$ are the points whose ordinate is $0 .$
$iii.$ Clearly, the distance of points $H$ and $D$ from $y -$axis is $5$ units and both lien in second and third quadrants respectively.
So, $(-5,-3)$ and $D(-5,1)$ are the points whose abscissa is $-5 .$

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Question 93 Marks

A point lies on the $x-$axis at a distance of $7$ units from the $y-$axis. What are its coordinates? What will be the coordinates if it lies on $y-$axis at a distance of $-7$ units from $x-$axis?

Answer

Given, point lies on the positive direction of $X$ -axis, so its $y$ -coordinate will be zero and it is at a distance of $7$ units from the $X$ axis, so its coordinates are $(7,0)$. If it lies on negative direction of $X$-axis, then its $x$-coordinate will be zero and its distance from $X$-axis is $7$ units, so its coordinates are $(0,-7)$.

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Question 103 Marks

Plot the following points and check whether they are collinear or not:
(1, 3), (-1, -1), (-2, 3)

Answer

Plotting the points P (1, 3), Q (-1, -1) and R (-2, -3) on the graph paper and join these points, we get a straight line. Hence, these points are collinear.

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Question 113 Marks

Write the coordinates of the vertices of a rectangle whose length and breadth are $5$ and $3$ units respectively, one vertex at the origin, the longer side lies on the $x$-axis and one of the vertices lies in the third quadrant.

Answer

Given length of rectangle $=5$ units Given breadth of rectangle $=3$ units One vertex is at origin i.e.., $D(0,0)$ and one of the other vertices lies in III quadrant. So the Length of the rectangle is $5$ units in the negative direction of $X$ -axis and then vertex is $A (-5,0)$.Also the breadth of the rectangle is $3$ units in the negative direction of $Y$ -axis and then vertex is $C(0,-3)$. The fourth vertex $B$ is $(5,-3)$.

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Question 123 Marks

Plot the points $(x, y)$ given by the following table. Use scale $1\ cm = 0.25$ units.

$x$	$1.25$	$0.25$	$1.5$	$-1.75$
$y$	$-0.5$	$1$	$1.5$	$-0.25$

Answer

Let $X’OX$ and $X’ OX$ be the coordinate axes. Plot the given points $(1.25, -0.5), (0.25, 1), (1.5,1.5)$ and $(-1.75, -0.25)$ on the graph paper.

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Maths 3 Marks Question

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