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Class 9 Maths Chapter 7 HOTS Questions - Coordinate Geometry
Question 1. From the following figure write:
(i) the points whose abscissa is 0.
(ii) the points whose ordinate is 0.
(iii) the points whose abscissa is –5
Ans: In an ordered pair (x, y), the first entry ‘x’ is the abscissa and the second entry ‘y’ is the ordinate of the point. Let us prepare the following table of ordered pairs of the given points. Also let us write their respective abscissa and ordinate.
From the table we get:
(i) Points with abscissa = 0 [that is x=0] are: A(0, 3), L(0, -4), and O (0,0).
(ii) Points with ordinate = 0 [that is y=0] are: G (5, 0), I(-2, 0), and O (0,0).
(iii) Points with abscissa = –5 [that is x= -5] are: D (-5, 1), H(-5, -3).
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FAQs on Class 9 Maths Chapter 7 HOTS Questions - Coordinate Geometry
| 1. What is the distance formula in coordinate geometry? |  |
Ans.The distance formula is used to determine the distance between two points in a Cartesian plane. The formula is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
| 2. How do you find the midpoint between two points in coordinate geometry? | |
Ans.The midpoint between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the midpoint formula:
\[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
This gives the coordinates of the point that is exactly halfway between the two points.
| 3. What is the slope of a line, and how is it calculated using coordinates? | |
Ans.The slope of a line is a measure of its steepness and is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are two distinct points on the line. A positive slope indicates the line rises, while a negative slope indicates it falls.
| 4. How can you determine if three points are collinear in coordinate geometry? | |
Ans.Three points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are collinear if the area of the triangle formed by them is zero. This can be verified using the determinant formula:
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| = 0 \]
If the area equals zero, the points are collinear.
| 5. What are the equations of lines in slope-intercept form and point-slope form? | |
Ans.The equation of a line can be represented in two common forms:
1. Slope-intercept form:
\[ y = mx + b \]
where \(m\) is the slope and \(b\) is the y-intercept.
2. Point-slope form:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
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