Slopes and Angles of a Line in an Orthonormal System
Published:
**Exercise 8:**
In an orthonormal system $(x'Ox \ ; \ y'Oy)$ consider the points $A(0 \ ; \ 2)$ and $B(3 \ ; \ -1)$.
1) Find the slope of straight line $(AB)$.
2) Find the value of the acute angle $\alpha$ formed by $(AB)$ and $x'Ox$.
3) Deduce the value of the acute angle $\beta$ formed by $(AB)$ and $y'Oy$.
Animated Video Solution
The first half plays free, the full solution is in the app.
Step by Step Written Solution
In this problem, we are working with an orthonormal system and two points, A at zero two, and B at three negative one. We need to find the slope of line A B, and the angles it forms with the coordinate axes.
Coordinate Geometry Problem
For the first part, let's calculate the slope m of the straight line A B using the slope formula.
1) Slope of (AB)
Plugging in our coordinates, we have negative one minus two over three minus zero.
This simplifies to negative three over three, which results in a slope of negative one.
Now for part two, we need the acute angle alpha formed by the line A B and the x-axis. We know the relationship between slope and the angle is that the slope equals the tangent of the angle of inclination.
2) Angle $\alpha$ with x'Ox
Since the slope is negative one, the angle of inclination theta is one hundred and thirty-five degrees. However, the question asks for the acute angle alpha.
The rest of this solution is on Solvi
5 more steps are locked. Watch the full animated, narrated solution for free.
Snap a photo, solve any question like this.
Watch the Rest for Free
Free to download · First solutions are on us
