Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Total Exercises: 5
Type: Notes
| TITLE | SOLUTION |
|---|---|
| Exercise 4.1 | View |
| Exercise 4.2 | View |
| Exercise 4.3 | View |
| Exercise 4.4 | View |
| Exercise 4.5 | View |
In this chapter we will read these topics:
- What are the meanings of the word geometry?
- Who was the founder of geometry.
- What is Plane geometry.
- What is Solid geometry.
- What is analytic geometry?
- Define a coordinate plane and coordinate axes.
- Define abscissa and ordinate of a point.
- Define quadrants.
- State and prove distance formula.
- Distance of point P(x,y) from x-axis is |y| and from y-axis is |x|.
- Distance measured non-parallel to coordinate axes is called undirected distance.
- Distance measured parallel to the coordinate axes is called directed distance.
- State and prove the Ration formula or Division formula.
- State and prove the Ration formula/Division formula for external division.
- Derive mid-point formula from ratio formula.
- Define Median of a triangle.
- What do you mean by concurrent lines.
- Define Centroid of a triangle.
- Show that medians of a triangle are concurrent.
- What are coordinates of centroid of a triangle.
- Define angle bisector and in-center of a triangle.
- Define the translation of axes.
- Write the equations of translation of axes.
- Define the rotation of axes.
- Write the equation of axes.
- Write the equation of rotation of axes.
- Define the inclination of a line.
- Define the slope or gradient of a line.
- Write formula for slope of a line passing through two points.
- What is the condition of two parallel lines.
- What is the condition of two perpendicular lines.
- When three points are said to be colinear.
- What is the equation of line parallel to x-axis.
- What is the equation of line parallel to y-axis.
- What do you mean by intercepts.
- State and prove the equation of line in slop-intercept form.
- Types of lines.
- State and prove equation of line in point-slope form.
- Derive the symmetric form of a line.
- State and prove equation of line in two-points form.
- Equation of non-vertical straight line passing through two points.
- State and prove equation of line in intercept form.
- State and prove equation of line in normal form.
- Describe the position of a point with respect to line.
- Point of intersection and condition of concurrent.
- Prove that altitudes of a triangle are concurrent.
- Prove that the right bisector of triangle are concurrent.
- Angle between two lines.
- Two lines l1 and l2 are parallel if and only if m1=m2.
- Find point of intersection of the lines.
- Find equation of line.
- Find acute angle.
- Find interior angles of triangles.
- Find interior angle of the quadrilateral.
- Find the center of the circumcircle of the triangle.
- Define the homogeneous equation of degree n in x and y variables.
- Define general homogeneous equation of second degree in x and y variables.
- Find a joint equation of the lines through the origin and perpendicular to the lines.
- Find the area of the bounded region.
- Area of tapezium