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Where will you find all points with positive abssissa and negative ordinate ?
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We will find all points with positive abssissa and negative ordinate in quadrant IV.
Write whether the following statements are true or false. Justify your answer.
(i) Point (5, 0) lies in the first quadrant.
(ii) The coordinates of the point whose ordinate is \(\dfrac{1}{2} \) and abscissa is 1 are \(\left(\dfrac{1}{2},1\right) \).
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(i) No, point lies on the xaxis
(ii) No, the coordinates will be as the coordinates are in the form
What is the perpendicular distance of the points A(7, – 4) from (i) xaxis (ii) yaxis ?
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(i) From xaxis it is 7 units in the +ve direction
(ii) From yaxis it is 4 units
In figure, ABDC is a square. Find the coordinates of points A and D.
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If we plot the given points in the graph and take the reflection of the points with respect to xaxis and yaxis we get A and D coordinates.
In the figure, if \(\triangle \) ABC and \(\triangle \) ABD are equilateral, then find the coordinates of points C and D.
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As ABC and ABD are equilateral triangle. So all sides will be
In the figure, ABCD is a square of side 2a. Find the coordinates of the vertices of the square :
(i) Taking AB and AD as axes.
(ii) Taking the centre of the square as origin and axes parallel to the sides AB and AD.
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(ii) Side
Centre
Coordinate of
Coordinate of
Plot the following points and write the name of the figure thus obtained.
A (–3, 2), B (–7,– 3), C (6, – 3), D (2, 2)
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Let X’ OX and Y’ OY be the coordinate axes and mark point on it. Here, point A(3,2) lies in II quadrant, B(7,3) lies in III quadrant, C(6, 3) lies in IV quadrant and D(2,2) lies in I quadrant. Plotting the points on the graph paper, the figure obtained is trapezium ABCD.
Plot the following points and check whether they are collinear or not.
(i) (0, 0), (2, 2), (5, 5)
(ii) (1, 3), (– 1, – 1), (–2, – 3)
(iii) (1, 1), (2, – 3), (–1, – 2)
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(i) From the graph, we find that all the three points lie on the same straight line. Hence, the given points are collinear.
(ii) From the graph, we find that all the three points lie on the same straight line. Hence, the given points are collinear.
(iii) From the graph, we find that all the three points do not lie on the same straight line. Hence, the given points are not collinear.
In the figure, \(\triangle \) PQR is an equilateral triangle with coordinates of vertices Q and R as (–2, 0) and (2, 0). Find the coordinates of the vertex P.
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vertices of
So
Coordinates of
The following table gives the number of pairs of shoes and their corresponding price. Plot these as ordered pairs and join them. What type of graph do you get ?
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We get bargraph
In the figure, AOB is a triangle with coordinates of A and O as (4,0) and (0,0) respectively. AB = 5. Find the coordinates of B.
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In
Coordinates of
In the figure, \(\triangle \) ABC is an equilateral triangle with coordinate of B and C as B (1, 0) and C (5, 0). Find the coordinate of vertex A.
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Three vertices of a rectangle are (– 4, 5), (– 4, 2) and (3, 2). Plot these points and find the coordinates of the fourth vertex.
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and
Points A (5, 3), B (–2, 3) and D (5, –4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.
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Coordinates of C are
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 xaxis and one of the vertices lies in the third quadrant.
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Let the rectangle be OABC with the vertex O at the origin.
Let OA be the longer side.
The coordinate of O is O(0,0).
Since one of the vertex is in the third quadrant and the longer side of length 5 units lie on the xaxis, the coordinate of A is A(−5,0).
Also, the rectangle lie in the III quadrant.
The side OC will lie on the yaxis to the negative direction.
Then, the length of OC is 3 units.
The coordinates of C will be C(0,−3).
Then obviously, the coordinates of B will be (−5,−3).
Here, OC  AB and AOC = , hence is a rectangle.
Therefore, the vertices of the rectangle are O(0,0), A(−5, 0), B(−5, −3), C(0, −3).