Ananya made a large trapezium by joining four equal trapeziums as shown in the figure. Find the coordinates of the vertices of all these trapeziums.

From the figure, the length of eight squares is 16 units. So, the side of each square = 16 8 = 2 units. We know that, the distance from any point to the x -axis is called y -coordinate and the distance from any point to the y -axis is called x -coordinate. Let us assume that, the vertices of blue colour trapezium be O , A , B and C . So, the coordinates of the trapezium O A B C are O ( 0 , 0 ) , A ( 4 , 4 ) , B ( 8 , 4 ) , C ( 8 , 0 ) .Let us assume that, the vertices of violet colour trapezium be B , C , D and E So, the coordinates of the trapezium B C E D B ( 8 , 4 ) , C ( 8 , 0 ) , E 16 , 0 , D 12 , 4 . And, the vertices of yellow trapezium be A , D , G and F . So, the coordinates of the vertices trapezium A D G F are A ( 4 , 4 ) , D ( 12 , 4 ) , G ( 12 , 8 ) , F ( 8 , 8 ) . And also assume that, the vertices of pink colour trapezium be D , E , H and G . So, the coordinates of trapezium D E H G are D ( 12 , 4 ) , E ( 16 , 0 ) , H 16 , 8 G ( 12 , 8 ) .

On environment day, class 9 students got six plants of mango, peepal, silver oak, banyan, amla and neem from soil department. Students planted the plants and noted their locations as x , y . Mango Peepal Silver oak Banyan Amla Neem x 3 3 0 - 3 - 3 0 y 0 4 7 4 0 - 3 Plot the points x , y in the graph and join them in the given order. Name the figure you get.

The given location of the plants are, Mango M Peepal P Silver oak S Banyan B Amla A Neem N x 3 3 0 - 3 - 3 0 y 0 4 7 4 0 - 3 We want to plot these points in the coordinate plane. First, we draw the coordinate axes, and choose our units such that one centimetre represents one unit on both the axes. The coordinates of the point M 3 , 0 tell us that the distance of this point from the y - axis along the positive x - axis is 3 units and the distance of the point from the x - axis is 0 units i.e., the point lies on the x - axis. Now, we start from the origin O , we count 3 units on the positive x - axis and mark the corresponding point as M . So, M is the position of the point 3 , 0 . The coordinates of the point P 3 , 4 tell us that the distance of this point from the y - axis along the positive x - axis is 3 units and the distance of the point from the x - axis along the positive y - axis is 4 units. Now, we start from the origin O , we count 3 units on the positive x - axis and we move in the positive direction of the y - axis and count 4 units and mark the corresponding point as P . So, P is the position of the point 3 , 4 . Similarly, we plot the other points S 0 , 7 , B - 3 , 4 , A - 3 , 0 and N 0 , - 3 and join all the points in the given order. The figure is shown in the below graph: Hence, by joining the points, the figure so formed is a hexagon.

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You are lucky enough to have found the only surviving copy of a treasure map left by the notorious pirate Short James Platinum - scourge of the seven seas. He has buried many pieces of treasure on the island - each in different location.

The Tsarina's Tiara is buried due north of Kaspar's cave. It is as far from Kaspar's cave to the Tiara as it is from Mermaid Pool to Trader's Bay. The coordinates of the place where the Tsarina's Tiara is buried is

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Important Questions on Coordinate Geometry

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9th CBSE

IMPORTANT

THINK ABOVE AND BEYOND MATHEMATICS PRACTICE BOOKS>Chapter 3 - Coordinate Geometry>Exercise>Q 9

Ananya made a large trapezium by joining four equal trapeziums as shown in the figure.

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Find the coordinates of the vertices of all these trapeziums.

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THINK ABOVE AND BEYOND MATHEMATICS PRACTICE BOOKS>Chapter 3 - Coordinate Geometry>Exercise>Q 10

Shown below is the seating arrangement in a classroom in $X - Y$ plane. The teacher’s position is the origin of $X - Y$ plane.

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Pooja’s position is given as $(1, - 1)$ , then Ravi and Surya's position (respectively) are

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THINK ABOVE AND BEYOND MATHEMATICS PRACTICE BOOKS>Chapter 3 - Coordinate Geometry>Exercise>Q 11

You are lucky enough to have found the only surviving copy of a treasure map left by the notorious pirate Short James Platinum - scourge of the seven seas. He has buried many pieces of treasure on the island - each in different location.

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Find the perpendicular distance of the place Skull Rock from the $x -$ axis.

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THINK ABOVE AND BEYOND MATHEMATICS PRACTICE BOOKS>Chapter 3 - Coordinate Geometry>Exercise>Q 12

Anmol loved to fly kites on Sankranti. He won a kite from the opponent and brought it with him to his home. He placed it on his big graph sheet such that the meeting point of the two diagonals was on the origin. He saw that it is in the shape of a Rhombus.

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If the length of the longer diagonal was measured with scale and found to be $10 cm$ and the shorter one was $8 cm$ , then find the coordinates of $A, B, C, D$ .

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THINK ABOVE AND BEYOND MATHEMATICS PRACTICE BOOKS>Chapter 3 - Coordinate Geometry>Exercise>Q 13

If the co-ordinates of a point $M (- 2, 9)$ can also be expressed as $(1 + x, y^{2})$ where $y > 0$ , then find the quadrants in which the following points lie:

$P (y, x), Q (2, x), R (x^{2}, y - 1), S (2 x, - 3 y)$ .

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9th CBSE

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THINK ABOVE AND BEYOND MATHEMATICS PRACTICE BOOKS>Chapter 3 - Coordinate Geometry>Exercise>Q 14

On environment day, class $9$ students got six plants of mango, peepal, silver oak, banyan, amla and neem from soil department. Students planted the plants and noted their locations as $(x, y)$ .

	Mango	Peepal	Silver oak	Banyan	Amla	Neem
$x$	$3$	$3$	$0$	$- 3$	$- 3$	$0$
$y$	$0$	$4$	$7$	$4$	$0$	$- 3$

Plot the points $(x, y)$ in the graph and join them in the given order. Name the figure you get.

Important Questions on Coordinate Geometry

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