P(−2, 6), Q(4, 5) and R(6.5, 0) are three points on the coordinate plane

Question

The point which is farthest away from the origin is the point???

Answer 1

First, we know that point R is 6.5 units away from the origin because its coordinates tell us that it is 6.5 units directly to the right of the origin and 0 units vertically.

Next, to determine how far away point P is from the origin, we need to use the Pythagorean theorem.

Point P is at (-2,6). If we draw a line from the origin to this point, that will make the hypotenuse of the triangle. The other two sides of the triangle can be drawn by going two units to the left from origin to create the base of the triangle, and then up six units to create the third side.

Now that we have our triangle, we use the Pythagorean theorem to solve for the hypotenuse. This will be the distance point P is from the origin.

(-2)² + 6² = P²

4 + 36 = P²

40 = P²

√40 = √P²

6.3 ≈ P

Lastly, we calculate the distance Q is from the origin using the same technique we used to solve how far point P is from the origin using the Pythagorean theorem.

4² + 5² = Q²

16 + 25 = Q²

41 = Q²

√41 = √Q²

6.4 ≈ Q

Final answers:

R = 6.5 units away from the origin

P ≈ 6.3 units away from the origin

Q ≈ 6.4 units away from the origin

Answer 2

Use Pythagoras

P is √40

Q is √41

R is √42.25