Question

A right triangle with leg lengths of 4 and 3 units has to be positioned in the coordinate plane to write a coordinate proof. Which set of coordinates would make the prrof easier to complete.

Answer 1

A set of coordinates that would make the proof easier to complete is: d. (0,4), (0,0), (3,0).

In Mathematics and Geometry, Pythagorean's theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:

`c^2=a^2+b^2`

Where:

• a is the opposite side of a right-angled triangle.
• b is the adjacent side of a right-angled triangle.
• c is the hypotenuse of a right-angled triangle.

In order to determine the length of c, we would have to apply Pythagorean's theorem as follows;

`c^2=a^2+b^2\\\\c^2=4^2+3^2\\\\c=√(16+9)`

c = 5 units.

Since these coordinates (0,4), (0,0), (3,0) consist of an ordered pair that is located at the origin (0, 0) with only positive integers, it represents a set of coordinates that would make the proof easier to complete.

Complete Question:

A right triangle with leg lengths of 4 and 3 units has to be positioned in the coordinate plane to write a coordinate proof.

Which set of coordinates would make the proof easier to complete?

a. (4,0), (0,0), (4,3)

b. (3,0), (0,0), (-4,0)

c. (0,4), (0,0), (-3,0)

d. (0,4), (0,0), (3,0)

Answer 2

We recommend to use a rectangular set of coordinates to make the proof easier to complete.

Explanation:

A right triangle is a triangle whose leg are orthogonal to each other, then we need to use a set of coordinates whose axes are orthogonal to each other. Hence, we recommend to use a rectangular set of coordinates to make the proof easier to complete.