Final answer:
The distance between point (0, a) and point (a, 0) is found using the distance formula derived from the Pythagorean theorem and equates to a√2. This is the length of the hypotenuse formed by a right triangle with sides of length a on the coordinate plane.
This correct answer is O √22²
Step-by-step explanation:
The distance between point (0, a) and point (a, 0) on a coordinate grid can be calculated using the distance formula, which is derived from the Pythagorean theorem.
Since the points lie on a coordinate plane, they form a right triangle with the distance between the points representing the hypotenuse of the triangle.
The change in x (horizontal distance) is a - 0 = a, and the change in y (vertical distance) is 0 - a = -a. The negative sign indicates direction, but since distance is a magnitude, it will be squared, making the sign irrelevant.
The distance is calculated as follows:
Square the change in x: a2
Square the change in y: (-a)2
Add the squares of the changes: a2 + a2
Take the square root of the sum: √(a2 + a2)
Simplify the expression: √(2a2)
Resulting distance: √2a
This simplifies to a√2, which is the distance between the two points on the coordinate grid.
This correct answer is O √22²