Determine whether the three points are the vertices of a right triangle. (-6,-4),(0,-2),(-10,8)

Name: Problem 23, Chapter 2: Precalculus
Uploaded: 2021-03-10T10:07:55-08:00
Duration: 2 min 47 s
Channel: K Joseph
Description: Determine whether the three points are the vertices of a right triangle. (-6,-4),(0,-2),(-10,8)

Determine whether the three points are the vertices of a...

Key Concepts

Distance Formula

The Distance Formula is used to calculate the distance between two points in the coordinate plane. It is derived from the Pythagorean Theorem and is essential for finding the lengths of the sides of a triangle when the coordinates of its vertices are known.

Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is used to determine whether a given triangle is a right triangle by verifying if this relation holds true for the side lengths.

Slope and Perpendicular Lines

The concept of slope refers to the steepness or incline of a line. In the coordinate plane, two lines are perpendicular if the product of their slopes is -1. This property is useful for checking the presence of a right angle in a triangle by confirming whether two sides are perpendicular.

Transcript

00:02 For the given question solution for the given question by seeing the question we have to say whether the given three points are right angle triangle right triangle or not so the points are this are the three point first point second point third point this is at the three point to find out whether it is a right triangle or not we'll use the distance between two points formula it may assume this is a bc the distance between a distance between and 2 points formula is square root of x2 minus x1 whole square plus y 2 minus y 1 whole square now we'll do ab b c c a next we'll do ab 2 points this ab 2 points apply the formula a b is equal to square root of in a x1 .1 b x2 y2 a x1 1 by 2 just have do it that is 0 minus of minus x plus 6 plus x plus y 2 is and minus 2 minus of minus 4 4 square now simplify this what you'll get that is 6 plus 4 will get so 40 square root 40 similarly b c and c will do same points bc will assume b is x1 y1 here b is x1 1 y1 c is x2 similarly i will do i will get this square root of under square root will get this now simplify this if you simplify this what will get 100 plus uh hundred will get correct 10 square plus 10 square square square two hundred will get similarly c also will do c is minus 10 comma 8 a is minus 6 comma minus 4 c a if you do what will get square root of minus 10 plus 6 whole square plus 8 plus 4 whole square now simplify this we'll get like this minus 10 plus 6 is minus 4 whole square 16 12 square it is uh 14 square root 24 square root 16 you get now according to 16 with the pythagoras theorem if it is satisfies then it is a right angle triangle by the other starstere is bc square is equal to basis square actually here bc square is equal to ab square plus c a square what is the basic root 200 whole square is equal to square root 40 old square like this will get next square and root will get cancelled square one will get cancelled and it's 200 is equal to 40 plus 160 200 will get so 200 is equal to 200 so the answer as for the georgation is the rewin...

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