Category: Straight lines

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DISTANCE FROM A POINT TO THE GIVEN LINE

Consider a point P(x1, y1) and a line in the line co – ordinate axes. The coordinates of points A and B are and . Area of   Example: Find the distance from the point (1, 2) to the line .   The required distance = units.

EQUATION OF A STRAIGHT LINE IN PARAMETRIC FORM

Consider a line AB makes an angle with the positive direction of x – axis and a point on the line is . Let a general point P on the line AB and the distance between P and Q is r. Draw a line QL, PM perpendicular to x-axis and draw. In a right angled […]

EQUATION OF A STRAIGHT LINE IN NORMAL FORM

Definition A normal to a line is a line segment drawn from a point perpendicular to the given line. Let p be the length of perpendicular form from the origin to a line, which subtends an anglewith the positive direction of x-axis as shown below: Let AB be a straight line on coordinate axes. p […]

EQUATION OF A LINE IN DEFFERENT FORMS

1. Slope-intercept form: Consider AB a straight line making an angle\(\displaystyle \theta \)with x-axis and cutting off an intercept OD=c from OY. As the line makes intercept OD=c on the y-axis, it is called as y-intercept. Consider the line AB intersect OX’ at T. Take a point P (x, y) on the line AB. Draw\(\displaystyle […]

EQUATION OF A LINE IN INTERCEPT FORM

The equation of a line which cuts off the given intercept on both the coordinate axes is determined as follows: Let PQ be a line meeting x-axis in A and y-axis in B. Consider OA = a, and OB = b. Then, the coordinates of A and B is. The equation of line joining A […]

ANGLE BETWEEN TWO LINES

Consider two lines: and , where , Angle between both lines are . Taking tan both sides,     Example Find the angle between the lines.   Solution The equation is written as follows: The angle between two lines is: we know that, substitute the values as follows: Therefore, the angle between two lines is. […]

EQUATION OF A LINE PARALLEL TO AXES

1. The equation of line parallel to the x-axis Consider the figure as shown below The equation of a line parallel to x – axis is y = y – intercept. For example a line whose y – intercept C is y = C. 2. The equation of line parallel to the y-axis Consider the […]

AREA OF A TRIANGLE

Consider a triangle as shown below: The most common formula to find the area of the triangle is. In any triangle, the area of the triangle is given by Where, b is the length of the base of the triangle and h is the length of the altitude drawn to an extension from the base. […]

SECTION FORMULA

1. Internal division Consider a point P(x, y) divides the line segment joining A(x1, y1) and B(x2, y2) in the ratio m : n. Draw   The coordinates of point P are   Example: Find the coordinates of point P which divides the line segment joining A(5, 3) and B(2, 1) in the ratio 5 […]

DISTANCE FORMULA

The perpendicular distance of a point from the y-axis is called x-coordinate and the perpendicular distance of a point from the x-axis is called y-coordinate. The coordinates of a point on the x-axis is in form of (x, 0) and the point on the y-axis is in the form of (0, y). The x – […]

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