The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two given points (2, 7) and (-2, 0) can be thought of as the coordinates of two vertices of a right triangle. The length between these two points can be calculated as the hypotenuse of this right triangle.
To find the length between (2, 7) and (-2, 0), we need to calculate the length of the horizontal side (the base) and the length of the vertical side (the height) of the right triangle formed by these two points.
The length of the base can be calculated as the difference between the x-coordinates of the two points: -2 - 2 = -4.
The length of the height can be calculated as the difference between the y-coordinates of the two points: 0 - 7 = -7.
Next, we can use the Pythagorean Theorem to find the length between these two points:
Length^2 = base^2 + height^2
Length^2 = (-4)^2 + (-7)^2
Length^2 = 16 + 49
Length^2 = 65
Taking the square root of both sides, we find:
Length ≈ √65 ≈ 8.06
Therefore, the length between (2, 7) and (-2, 0) is approximately 8.06 units.
Apply the Pythagorean Theorem to find the length between (2,7) and (−2, 0) Round your answer to the nearest hundredth, if necessary.(1 point)
1 answer