In which quadrant or on which axis do each of points (-, 2,, 4) , (3, ,-, 1) , (-, 1,, 0) , (1,

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3. Coordinate Geometry

easy

In which quadrant or on which axis do each of the points $(-\, 2,\, 4)$, $(3, \,-\, 1)$, $(-\, 1,\, 0)$, $(1,\, 2)$ and $(-\, 3, \,-\, 5)$ lie ? Verify your answer by locating them on the Cartesian plane.

Option A

Option B

Option C

Option D

Solution

In the point $(-\,2,\,4),$ the abscissa is negative and the ordinate is positive.

$\because (-,\,+)$ belongs to $2nd$ quadrant.

$\therefore $ $(-\,2,\,4)$ lies in the second quadrant.

The point $(3,\,-1)$ is having $+ ve$ abscissa and $-\,ve$ ordinate.

$\therefore \,(3,\,-\,1)$ lies in the $4 th$ quadrant.

The point $(-\,1,\,0)$ is having $(- \,ve )$ abscissa and ordinate on the $x$ -axis.

$\therefore$ The point $(-\,1,\,0)$ lies on the negative $x$ -axis.

The point $(1,\,2)$ is having the $x$ – coordiante as well as $y$ – coordinate $+\,v e .$

$\therefore$ Point $(1,\,2)$ lies in the list quadrant.

The point $(-\,3,\,-\,5)$ is having the abscissa as well as ordinate negative.

$\therefore$ Point $(-\,3,\,-\,5)$ lies in the $3 rd$ quadrant.

These points are plotted in the Cartesian plane as shown in the following figure as $A\, (-\,2,\,4)$ ; $B \,(3,\,-\,1)$ $C\, (-\,1,\,0) $; $D \,(1,\,2)$ and $E \,(-\,3,\,-\,5)$.

Standard 9

Mathematics

See Fig. and complete the following statements :

$(i)$ The abscissa and the ordinate of the point $B$ are ……… and ……… respectively. Hence, the coordinates of $B$ are (……… , ………)

$(ii)$ The $x$ -coordinate and the $y$ -coordinate of the point $M$ are ……… and ……… respectively. Hence, the coordinates of $M$ are (……… , ………)

$(iii)$ The $x$ -coordinate and the $y$ -coordinate of the point $L$ are ……… and ……… respectively. Hence, the coordinates of $L$ are (……… , ………)

$(iv)$ The $x$ -coordinate and the $y$ -coordinate of the point $S$ are ……… and ……… respectively. Hence, the coordinates of $S$ are (……… , ………)

medium

Plot the following ordered pairs $(x,\, y)$ of numbers as points in the Cartesian plane. Use the scale $1\,cm = 1$ unit on the axes.

$x$ $-3$ $0$ $-1$ $4$ $2$

$y$ $7$ $-3.5$ $-3$ $4$ $-3$

easy

Locate the points $(5, \,0)$, $(0,\, 5)$, $(2,\,5)$, $(5,\, 2)$, $(-\,3, \,5)$, $(-\,3, \,-\,5)$, $(5,\, -\,3)$ and $(6,\, 1)$ in the Cartesian plane.

easy

(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are $200 \,m$ apart. There are $5$ streets in each direction. Using $1\,cm = 200 \,m$, draw a model of the city on your notebook. Represent the roads/streets by single lines.

There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North – South direction and another in the East – West direction. Each cross street is referred to in the following manner : If the $2^{nd}$ street running in the North – South direction and 5th in the East – West direction meet at some crossing, then we will call this cross-street $(2, \,5).$ Using this convention, find :

$(i)$ how many cross – streets can be referred to as $(4,\, 3).$

$(ii)$ how many cross – streets can be referred to as $(3,\, 4).$

medium

Write the answer of each of the following questions :

$(i)$ What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane ?

$(ii)$ What is the name of each part of the plane formed by these two lines ?

$(iii)$ Write the name of the point where these two lines intersect.

easy

In which quadrant or on which axis do each of the points $(-\, 2,\, 4)$, $(3, \,-\, 1)$, $(-\, 1,\, 0)$, $(1,\, 2)$ and $(-\, 3, \,-\, 5)$ lie ? Verify your answer by locating them on the Cartesian plane.

Solution

Similar Questions

Plot the following ordered pairs $(x,\, y)$ of numbers as points in the Cartesian plane. Use the scale $1\,cm = 1$ unit on the axes. $x$ $-3$ $0$ $-1$ $4$ $2$ $y$ $7$ $-3.5$ $-3$ $4$ $-3$

Locate the points $(5, \,0)$, $(0,\, 5)$, $(2,\,5)$, $(5,\, 2)$, $(-\,3, \,5)$, $(-\,3, \,-\,5)$, $(5,\, -\,3)$ and $(6,\, 1)$ in the Cartesian plane.

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Plot the following ordered pairs $(x,\, y)$ of numbers as points in the Cartesian plane. Use the scale $1\,cm = 1$ unit on the axes.

$x$ $-3$ $0$ $-1$ $4$ $2$

$y$ $7$ $-3.5$ $-3$ $4$ $-3$