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Chapter Analysis
Intermediate24 pages • EnglishQuick Summary
This chapter on 'Straight Lines' covers the fundamental concepts of slopes, equations, and properties of straight lines in a plane. It delves into the different forms of line equations, conditions for parallelism and perpendicularity, and derives equations based on various parameters like slope-intercept and two-point forms. Additionally, it discusses the geometric interpretations like the distance of a point from a line and the area of triangles formed by lines.
Key Topics
- •Slope of a line
- •Equation of a line
- •Parallel and perpendicular lines
- •Distance from a point to a line
- •Different forms of line equations
- •Intercepts of a line
- •Collinearity of points
- •Area calculation of geometrical figures
Learning Objectives
- ✓Understand how to calculate the slope of a line between two points.
- ✓Learn to write the equation of a line in different forms.
- ✓Identify the conditions for parallel and perpendicular lines.
- ✓Calculate the distance of a point from a line.
- ✓Utilize the slope-intercept and point-slope forms to derive line equations.
Questions in Chapter
Exercise 9.1: Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
Page 158
Exercise 9.3: Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
Page 167
Miscellaneous Exercise: Find the values of k for which the line (k–3) x – (4 – k²) y + k² –7k + 6 = 0 is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin.
Page 173
Additional Practice Questions
What is the equation of a line parallel to the y-axis and passing through the point (3, -7)?
easyAnswer: The equation is x = 3, since a line parallel to the y-axis has the form x = constant.
Find the slope of a line passing through the points (2, 3) and (4, 11).
mediumAnswer: The slope m is calculated as (11 - 3) / (4 - 2) = 8 / 2 = 4.
Describe the conditions under which two lines are perpendicular in a plane.
easyAnswer: Two lines are perpendicular if the product of their slopes is -1.
A line makes an angle of 45° with the positive direction of the x-axis. What is its slope?
easyAnswer: The slope m of the line is tan(45°) = 1.
How do you find the equation of a line given a point (1, 2) and its slope 3?
mediumAnswer: Using the point-slope form, y - 2 = 3(x - 1), the equation simplifies to y = 3x - 1.