Namrata Das Exams Prep Master
Exams Prep Master
The study of geometric figures by plotting them in coordinate axes is known as coordinate geometry. Straight lines, curves, circles, ellipses, hyperbolas, and polygons can all be easily drawn and scaled in the coordinate axes. Further coordinate geometry aids in algebraic work and the study of the properties of geometric figures using the coordinate system. Here we have answered some important questions on the topic to ace your preparation.
The video below explains this:
Coordinate Geometry Detailed Video Explanation:
Check also: Coordinate Geometry MCQs
Very Short Answer Questions [1 Marks Question]
Ques. Which quadrant contains the points P(3,0), Q(6,0), R (-7.0), and S (0,-6)?
Ans. These points do not fall into any of the four quadrants. The points will be located on the axes.
Ques. Is P (3, 2) and Q(2, 3) the same point?
Ans. P(3,2) and Q(2,3) are not the same point. The first has an x component of 3 and a y component of 2, whereas the second has an x component of 2 and a y component of 3.
Ques. What is the name of the horizontal and vertical lines used to calculate the position of any point in the Cartesian plane?
Ans. The horizontal line is known as the x – axis, and the vertical line is known as the y – axis.
Ques. Name the plane points that do not fall into any of the quadrants.
Ans. The plane point which does not belong to any one of the quadrants is origin, which is denoted by O (0,0).
Ques. Write the coordinates of a point that is 3 units above the x-axis and lies on the y-axis.
Ans. The coordinates of a point on the y-axis that is 3 units above the x-axis is (0, 3).
Ques. Determine the abscissa and ordinate of a point (-3, -4).
Ans. These points are located on the axes.
Ques. Determine the distances between points C(-3, -2) and D(5, 2) on the x- and y-axes.
Ans. Point C(-3, -2) is 2 units away from the x-axis and 3 units away from the y-axis in the negative direction. Point D(5, 2) is 2 units away from the x-axis and 5 units away from the y-axis.
Ques. Write the mirror image of the points (2, 3) and (-4, -6) in relation to the x-axis.
Ans. With respect to the x-axis, the mirror image of point (2, 3) is (2, -3). With respect to the x-axis, the mirror image of (-4, -6) is (-4,6).
Short Answer Questions [2 Marks Questions]
Ques. Which axes do the given points fall on?
- (7, 0)
- (0, -3)
- (0, 6)
- (-5, 0)
Ans.
- Because the y component is zero, the point falls on the X-axis.
- Because the x component is zero, the point falls on the Y-axis.
- Because the x component is zero, the point falls on the Y-axis.
- Because the y component is zero, the point falls on the X-axis.
Ques. Which quadrants do the given points fall into?
- (4, -2)
- (-3, 7)
- (-1, -2)
- (3, 6)
Ans.
- Because the x component is positive and the y component is negative, the points fall into quadrant IV.
- Because the x component is negative and the y component is positive, the points fall into quadrant II.
- III quadrant because the x and y components are both negative.
- Quadrant I because the x component and the y component are both positive.
Ques. Write the name of each part of the plane formed by Vertical and horizontal lines.
Ans. The vertical line is called y-axis, the horizontal line is called x-axis. And these form four quadrants.
Ques. Write the Coordinates of a point which lies on the x-axis and is at a distance of 4 units to the right of origin. Draw its graph.
Ans. (4, 0)
Ques. Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis.
Ans. The mirror image of point (2, 3) is (2, -3) with respect to the x-axis.
The mirror image of (-4, -6) is (-4,6) with respect to the x-axis.
Ques. Write the Coordinates of a point which lies on the y-axis and is at a distance of 3 units above x-axis. Represent on the graph.
Ans. The Coordinates of the point which lies on the y-axis and at a distance of 3 units above the x- axis is (0, 3).
Ques. Which of the following points belong to the x-axis? (2, 0), (3, 3), (0, 1), (-2, 0)
Ans. (2, 0) and (-2, 0) belong to the x- axis.
To be on the x axis the y-component must be zero.
Long Answer Questions [3 Marks Questions]
Ques. Make a triangle with the vertices 0(0,0), A(3,0), and B. (3,4). Determine the triangle's classification as well as its area.
Ans. The Triangle is a right angle triangle.
The triangle's area is half of the product of its base and height, or 6 square units.
Ques. In the Cartesian plane, locate the points (5, 0), (0, 5), (2, 5), (5, 2), (-3, 5), (-3, -5), and (6, 1)
Ans. The points on the Cartesian plane will be:
Ques. In a Cartesian plane, find the points (A) (-3, 4) (B) (3, 4) and (C) (0, 0) and write the name of the figure formed by joining them.
Ans. The formed figure is a Triangle.
Ques. On graph paper, draw the quadrilateral formed by joining (1, 1), (6, 1), (4, 5) and (3, 5).
Ans. After Plotting, it is a Trapezium.
Very Long Answer Questions [5 Marks Questions]
Ques. The table below shows the relationship between natural numbers and odd natural numbers.
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| y | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
Plot and connect the points. By connecting these points, do you get a straight line?
Ans. Yes, joining these points results in a straight line.
Ques. Plot the following points, connect them in the correct order, and identify the resulting figure: A(1, 3), B(1, -1), C(7, -1) and D (7, 3).
Calculate the coordinates of the diagonals' point of intersection.
Ans. ABCD will form a rectangle.
The point at which the diagonals AC and BD intersect is (4, 1).
Ques. Write the coordinates of two X-axis points and two Y-axis points that are equal distances from the origin. Connect all of these points to form the quadrilateral's vertices. Name the resulting quadrilateral.
Ans. Allow a to be the same distance from the origin on both axes. The coordinates of two points on the x-axis with equal distance 'a' are now P (a, 0) and R (-a, 0). In addition, the coordinates of two points on the Y-axis with equal distance 'a' are Q(0, a) and S. (0, -a). Connect all four points on the graph. PQRS is now formed as a square.
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