Calculating Line Slope Angle
To find the angle of the slope, we first need to determine the slope ($m$) of the line passing through the points $(3, 4)$ and $(4, 5)$.
Finding the Slope
The formula for the slope ($m$) given two points $(x_1, y_1)$ and $(x_2, y_2)$ is:
$ m = \frac{y_2 - y_1}{x_2 - x_1} $
Substituting the given points:
$ m = \frac{5 - 4}{4 - 3} $
$ m = \frac{1}{1} $
$ m = 1 $
Determining the Angle of Slope
The slope ($m$) of a line is also equal to the tangent of the angle of inclination ($\theta$) it makes with the positive x-axis.
$ m = \tan(\theta) $
We found the slope $m = 1$. Therefore:
$ \tan(\theta) = 1 $
To find the angle $\theta$, we take the arctangent (inverse tangent) of 1:
$ \theta = \arctan(1) $
The angle whose tangent is 1 is $45^\circ$.
$ \theta = 45^\circ $
Similar Questions
- Find the relation between x and y such that the point (x, y) is equidistant from (6, 2) and (4, 6).
- Find the area of a triangle formed by $(1, 0)$, $(-1, 0)$, $(0, 1)$.
- The points A (1, 2), B (3, 4) and C (4, 1) are the vertices of a triangle which is:
- Three straight lines $x + y - 3 = 0$, $x + y + 2 = 0$ and $3x + 3y - 7 = 0$ are:
- The image of the point $(7, 8)$ when reflected along the x-axis is:
- The equation of a straight line passing through (-2,5) and (1,3) is:
- The intercepts made by the plane $3x - 4y - 2z = 6$ with the coordinate axis are:
- Find the relation between x and y such that the point (x, y) is equidistant from (5, 3) and (4, 6).
- The distance between two points $(a \cos \alpha, 0)$ and $(0, a \sin \alpha)$ is_____.
- The area of the triangle formed by the line $2x - 4y - 7 = 0$ with the coordinate axis is:
Important Questions from Coordinate Geometry
What is the reflection of the point (-1, 5) in the line x = 1?
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
Slope of the line AB is 4/3. Co-ordinates of points A and B are (x, -5) and (2, -3) respectively. What is the value of x?
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
