Investigate if the triangle with the corners ABC is right-angled, when the corners are in the coordinates A (4, -4), B (11, -1) and C (9,3).
Does this mean simply plot it out on a graph paper and see? Or is there some sort of math towards doing this that doesn't require drawing it down.
Yeah, it means to plot the points and then say if it is a right-angled triangle.
no, they want you to take the slope of the 3 lines.
If one slope is the opposite reciprocal of another, then those two lines are perpendicular.
I will assume you know how to take slopes.
Plotting will help, it could show where angles are obviously not equal to 90°,
but suppose the lines make an angle of 89°, this would be hard to judge.
To determine if a triangle is right-angled, you can use the Pythagorean theorem or the slope of the sides of the triangle.
1. Using the Pythagorean theorem:
a) Find the lengths of all three sides of the triangle using the distance formula, which is given by:
- The distance between points A and B is √[(x2 - x1)² + (y2 - y1)²].
- The distance between points B and C is √[(x2 - x1)² + (y2 - y1)²].
- The distance between points A and C is √[(x2 - x1)² + (y2 - y1)²].
b) Once you have the lengths of the three sides (usually denoted as a, b, and c), apply the Pythagorean theorem:
- If a² + b² = c², then the triangle is right-angled.
- If a² + b² ≠ c², then the triangle is not right-angled.
2. Using the slopes of the sides:
a) Calculate the slopes of the two sides that form the right angle (usually denoted as m1 and m2). The slope formula is given by:
- The slope between points A and B is (y2 - y1) / (x2 - x1).
- The slope between points B and C is (y2 - y1) / (x2 - x1).
b) If the product of the slopes m1 * m2 = -1, then the triangle is right-angled.
- If m1 * m2 ≠ -1, then the triangle is not right-angled.
Both methods are valid ways to determine if a triangle is right-angled without drawing it.