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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, (y7)/(31) = (46)/(10)
y7 = 2
y = 9
The tangent of the angle which the part of the line above the Xaxis makes with the positive direction of the Xaxis 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 xaxis. Thus, if a line makes an angle θ with the positive direction of the xaxis, 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.
Slope of a line which cuts intercepts of equal lengths on the axes is:
The equation of line which cuts intercepts of equal lengths on the axes is:
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.
Since tan θ is not defined when θ = 90°, therefore, the slope of a vertical line is not defined. i.e., slope of yaxis 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
= (51)÷(2x) =2
51 = 42x
0 = 2x
x=0
If the slope of line m = tan 0°. Therefore, the line is _____ to the Xaxis.
Slope of xaxis is m = tan 0° = 0.
Since the inclination of every line parallel to xaxis 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 m_{1} and m_{2 }respectively.
Then,
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
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