Class 9 Maths Chapter 1 Orienting Yourself: The Use of Coordinates Worksheet

CORDINATE GEOMETRY Class 09 - Maths (Ganita Manjari) Time Allowed: 1 hour Maximum Marks: 93 1 . Figure shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked [5] in the fi gure. Point O is the origin. i . If D 1 R 1 represents the door to Reiaan's room, how far is the door from the left wall (the y- axis) of the room? How far is the door from the x -axis? (1) ii . What are the coordinates of D 1 ? (1) iii . If R 1 is the point (11.5, 0) , how wide is the door? Do you think this is a comfortable width for USP the room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily? (2) OR If B 1 (0, 1.5) and B 2 (0, 4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door? (2) 2 . On a graph sheet, mark the x -axis and y -axis and the origin O. Mark points from (−7, 0) to [5] (13, 0) on the x -axis and from (0, −15) to (0, 12) on the y-axis. (Use the scale 1 cm = 1 unit.) Using Figure, answer the given question- Place Reiaan's rectangular study table with three of its feet at the points (8, 9), (11, 9) and (11, 7) .

i . Where will the fourth foot of the table be? ii . Is this a good spot for the table? iii . What is the width of the table? The length? Can you make out the height of the table? 3 . On a graph sheet, mark the x -axis and y -axis and the origin O. Mark points from (−7, 0) to [3] (13, 0) on the x -axis and from (0, −15) to (0, 12) on the y -axis. (Use the scale 1 cm = 1 unit.) Using Figure, answer the given question- If the bathroom door has a hinge at B1 and opens into the bedroom, will it hit the wardrobe? Are there any changes you would suggest if the door is made wider?

4 . On a graph sheet, mark the x -axis and y -axis and the origin O. Mark points from (−7, 0) to [5] (13, 0) on the x -axis and from (0, −15) to (0, 12) on the y -axis. (Use the scale 1 cm = 1 unit.) Using Figure, answer the given question- USP Look at Reiaan's bathroom. i . What are the coordinates of the four corners O , F , R , and P of the bathroom? ii . What is the shape of the showering area SHWR in Reiaan's bathroom? Write the coordinates of the four corners. iii . Mark o ff a 3 ft × 2 ft space for the washbasin and a 2 ft × 3 ft space for the toilet. Write the coordinates of the corners of these spaces.

5 . On a graph sheet, mark the x -axis and y -axis and the origin O. Mark points from (−7, 0) to [3] (13, 0) on the x -axis and from (0, −15) to (0, 12) on the y -axis. (Use the scale 1 cm = 1 unit.) Using Figure, answer the given question- Other rooms in the house: i . Reiaan's room door leads from the dining room which has the length 18 ft and width 15 ft. The length of the dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners. ii . Place a rectangular 5 ft × 3 ft dining table precisely in the centre of the dining room. Write down the coordinates of the feet of the table.

6 . What are the x-coordinate and y-coordinate of the point of intersection of the two axes? [2] 7 . Point W has x-coordinate equal to -5. Can you predict the coordinates of point H which is on the [2] line through W parallel to the y-axis? Which quadrants can H lie in? 8 . Consider the points R (3, 0), A (0, −2), M (−5, −2) and P (−5, 2) . If they are joined in the [5] same order, predict: i . Two sides of RAMP that are perpendicular to each other. ii . One side of RAMP that is parallel to one of the axes.

iii . Two points that are mirror images of each other in one axis. Which axis will this be? USP Now plot the points and verify your predictions. 9 . Plot point Z (5, −6) on the Cartesian plane. Construct a right-angled triangle IZN and fi nd the [3] lengths of the three sides. (Comment: Answers may di ff er from person to person.) 10 . What would a system of coordinates be like if we did not have negative numbers? Would this [3] system allow us to locate all the points on a 2-D plane? 11 . Are the points M (−3, −4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method to [3] check this without plotting and joining the points.

12 . Use your method (from Problem 6) to check if the points R (−5, −1), B (−2, −5) and [3] C (4, −12) are on the same straight line. Now plot both sets of points and check your answers. 13 . Using the origin as one vertex, plot the vertices of: [5] i . A right-angled isosceles triangle. ii . An isosceles triangle with one vertex in Quadrant III and the other in Quadrant IV. 14 . Use the connection you found to fi nd the coordinates of B given that M (−7, 1) is the midpoint [3] of A (3, −4) and B ( x , y ) .

15 . Let P , Q be points of trisection of AB, with P closer to A, and Q closer to B. Using your knowledge [3] of how to fi nd the coordinates of the midpoint of a segment, how would you fi nd the coordinates of P and Q ? Do this for the case when the points are A (4, 7) and B (16, −2) . 16 . i . Given the points A (1, −8), B (−4, 7) and C (−7, −4) , show that they lie on a circle K whose [5] center is the origin O (0, 0) . What is the radius of circle K ? ii . Given the points D (−5, 6) and E (0, 9) , check whether D and E lie within the circle, on the circle, or outside the circle K.

17 . The midpoints of the sides of triangle ABC are the points D , E , and F . Given that the [5] coordinates of D , E , and F are (5, 1), (6, 5) , and (0, 3) , respectively, fi nd the coordinates of A, B and C. 18 . A city has two main roads which cross each other at the centre of the city. These two roads are [5] along the North-South (N-S) direction and East-West (E-W) direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 10 streets in each direction.

i . Using 1 cm = 200 m , draw a model of the city in your notebook. Represent the roads/streets by single lines. ii . There are street intersections in the model. Each street intersection is formed by two streets- one running in the N − S direction and another in the E-W direction. Each street intersection is referred to in the following manner: If the second street running in the N-S direction and 5th street in the E-W direction meet at some crossing, then we call this street intersection (2,5). Using this convention, fi nd:

a . how many street intersections can be referred to as (4, 3) . b . how many street intersections can be referred to as (3, 4) . 19 . A computer graphics program displays images on a rectangular screen whose coordinate system [3] has the origin at the bottom-left corner. The screen is 800 pixels wide and 600 pixels high. A circular icon of radius 80 pixels is drawn with its centre at the point A (100, 150) . Another circular icon of radius 100 pixels is drawn with its centre at the point B (250, 230) . Determine:

i . whether any part of either circle lies outside the screen. USP ii . whether the two circles intersect each other. 20 . Plot the points A (2, 1), B (−1, 2), C (−2, −1) , and D (1, −2) in the coordinate plane. Is ABCD a [5] square? Can you explain why? What is the area of this square? 21 . What is the x-coordinate of a point on the y-axis? [3] 22 . Is there a similar generalization for a point on the x-axis? [3] 23 . Does point Q (y, x) ever coincide with point P (x, y)? Justify your answer. [3] 24 . If x ≠ y , then ( x , y ) ≠ ( y , x ) ; and ( x , y ) = ( y , x ) if and only if x = y . Is this claim true? [3] 25 . In moving from A (3, 4) to D (7, 1) , what distance has been covered along the x -axis? What [2] about the distance along the y -axis?

26 . Would these observations be the same if △ ADM is re fl ected in the x-axis (instead of the y - [3] axis)?