Coordinate Geometry Grade IX Worksheet Solution

Self Assessment Test 3 - Solutions

Based on Chapter 3

1. Question: What are the signs of a point in 2nd quadrant?

   Solution: In the 2nd quadrant, the x-coordinate is negative and the y-coordinate is positive.

2. Question: What is the distance of the point \(A(-2,-3)\) from y-axis?

   Solution: The distance of a point \((x, y)\) from the y-axis is equal to the absolute value of its x-coordinate. So, the distance of point \(A(-2, -3)\) from y-axis is \(|-2| = 2\) units.

3. Question: Plot the points \(P(2,-1)\), \(Q(0,5)\), \(C(3,4)\) and \(D(-3,-5)\) in the cartesian plane.

   Solution: To plot these points on the cartesian plane, plot each point by counting spaces: Right and up for positive coordinates, left and down for negative coordinates. For example, to plot P(2, -1), move 2 spaces to the right and 1 space down from the origin.

4. Question: A point \(R\) is at a distance of 3 units from the x-axis and 7 units from y-axis and is in 3rd quadrant. Write the coordinates of \(R\).

   Solution: In the 3rd quadrant, both x and y coordinates are negative. Therefore, the coordinates of point \(R\) are \((-7, -3)\).

5. Question: Which of the following points lie in quadrant IV? \(L(3,-5)\), \(M(5,-3)\), \(N(-2,-1)\), \(P(1,2)\), \(Q(2,-7)\) and \(R(-1,-1)\)

   Solution: In the 4th quadrant, x is positive and y is negative. Therefore, points \(L(3, -5)\), \(M(5, -3)\), and \(Q(2, -7)\) lie in the 4th quadrant.

6. Question: Plot the points \(A(2,0)\), \(B(0,2)\), \(C(-2,0)\) and \(D(0,-2)\). What type of figure is ABCD ?

   Solution: After plotting these points on the cartesian plane, it can be observed that ABCD forms a square.

7. Question: Find the values of \(x\) and \(y\) if \((3x-7,2y+11)=(2x-3,2-y)\)

   Solution: From \(3x - 7 = 2x - 3\), we can find \(x = 4\). From \(2y + 11 = 2 - y\), we can find \(y = -3\).

8. Question: The points \(E(2,4)\), \(F(-5,4)\) and \(H(2,-3)\) are the vertices of a square EFGH. Plot the points on the graph paper and hence, find the coordinates of \(G\).

   Solution: The coordinates of \(G\) are \((-5, -3)\) as it will be diagonally opposite to \(E\) and have the same x-coordinate as \(F\) and the same y-coordinate as \(H\).

9. Question: Plot the points \((-4,-10)\),\((-2,-4)\),\((0,2)\),\((2,8)\) and \((4,14)\) and show that they are collinear.

   Solution: These points are collinear because the differences in the x-coordinates and y-coordinates are proportional: \(\frac{y_2-y_1}{x_2-x_1} = \frac{y_3-y_2}{x_3-x_2} = \ldots\) for collinear points. You can verify this by plotting them on graph paper.

10. Question: The following table gives the cost of different number of toys.

    \(x\) (number of toys)	2	4	6	8	10	12	15
    \(y\) (cost in ₹)	20	40	60	80	100	120	150

    Plot the points (as ordered pairs) and join them.

    Solution: Plot each point from the table as an ordered pair (x, y) on graph paper, such as (2, 20), (4, 40), etc., and join them to see the linear relationship between the number of toys and the total cost.