the graph line passing through (1,1) , (-2,4) make with positive x-axis angle equal is:
a) 30 degree
b) 45 degree
c) 60 degree
d) 135 degree
slope = (4-1)/(-2-1) = -1
If Ø is the angle that the line makes with the x-axis, then
tanØ = -1
Ø = 135°
(draw the line to verify)
To find the angle that the graph line passing through the points (1,1) and (-2,4) makes with the positive x-axis, we can use the slope of the line.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (1, 1) and (x2, y2) = (-2, 4).
slope = (4 - 1) / (-2 - 1)
slope = 3 / -3
slope = -1
The negative sign indicates that the line is sloping downwards.
The angle that a line makes with the positive x-axis can be found using the arctangent function:
angle = arctan(slope)
angle = arctan(-1)
Using a calculator, arctan(-1) ≈ -45 degrees.
However, since the question asks for the positive angle, we add 180 degrees to -45.
angle = -45 + 180
angle = 135 degrees
Therefore, the graph line passing through (1,1) and (-2,4) makes a 135-degree angle with the positive x-axis.
The correct answer is d) 135 degrees.
To find the angle the line makes with the positive x-axis, we first need to calculate the slope of the line.
The slope between two points (x₁,y₁) and (x₂,y₂) on a line is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's use the given points (1,1) and (-2,4) to find the slope of the line passing through them:
m = (4 - 1) / (-2 - 1)
= 3 / -3
= -1
The angle that the line makes with the positive x-axis can be found using trigonometry. The tangent of the angle is equal to the slope of the line.
tan(angle) = -1
Now, we need to find the value of the angle itself by taking the inverse tangent (arctan) of -1.
angle = arctan(-1)
Using a calculator or reference table, we find that the value of arctan(-1) is -45 degrees. However, since we are looking for the angle in the positive x-axis direction, we need to add 180 degrees to the angle:
angle = -45 + 180
= 135 degrees
Therefore, the line passing through (1,1) and (-2,4) makes an angle of 135 degrees with the positive x-axis.
The correct answer is option d) 135 degrees.