The value of y, for the line passing through (3, y) and (2, 7) is parallel to the line passing through (-1 , 4) and (0, 6) is:
As A(3,y) and B(2,7) is parallel to C(-1,4) and D(0,6)
∴ their slopes are equal
so, (y-7)/(3-1) = (4-6)/(-1-0)
y-7 = 2
The tangent of the angle which the part of the line above the X-axis makes with the positive direction of the X-axis is:
The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ.
Two lines are said to be parallel when the difference of their slopes is
Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope and lines with the same slope are parallel.
m1 and m2 are the slope of two perpendicular lines, if
If the lines are perpendicular to each other then their slopes are in the form m1.m2 = -1
The points A and B have coordinates (3, 2) and (1, 4) respectively. So, the slope of any line perpendicular to AB is
If the lines are perpendicular to each other then their slopes are in the form m1.m2 = -1.(since product of slopes of two perpendicular lines is -1) Therefore , m = 1.
Slope of a line is not defined, when q = ……
Since tan θ is not defined when θ = 90°, therefore, the slope of a vertical line is not defined. i.e., slope of y-axis is m = tan 90° = ∞ i.e., not defined.
If the slope of the line passing through the points (2, 5) and (x, 1) is 2, then x = ……
Slope=change in y coordinates÷change in x coodinates
If the slope of line m = tan 0°. Therefore, the line is …… to the X-axis.
Slope of x-axis is m = tan 0° = 0.
Since the inclination of every line parallel to x-axis is 0°, so its slope (m) = tan 0° = 0. Therefore, the slope of every horizontal line is 0.
If A (-2, 1), B (2, 3) and C (-2, -4) are three points, find the angle between the straight lines AB and BC.
Let the slope of the line AB and AC are m1 and m2 respectively.
Let θ be the angle between AB and BC. Then,
Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicular to the line AB is:
Slope of the points A and B is -2 and the lines are perpendicular then
m1×m2 = -1.
∴ the slope is 1/2