Final answer:
The distance between the points (1,3) and (9,20) is found using the Pythagorean Theorem to be √353, which represents the hypotenuse of the right triangle formed by the horizontal and vertical legs on a coordinate plane.
Step-by-step explanation:
To calculate the distance between the points (1,3) and (9,20) using the Pythagorean Theorem, we need to treat these points as coordinates on a Cartesian plane and find the length of the hypotenuse of the right triangle that they form with the distance being calculated along the hypotenuse.
First, we need to calculate the differences in the x-coordinates (Δx) and y-coordinates (Δy) which are the legs of the right triangle. Δx = 9 - 1 = 8 and Δy = 20 - 3 = 17.
According to the Pythagorean Theorem, which is a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides, the distance between the points, which is the length of the hypotenuse (c), will be:
c = √(Δx² + Δy²) = √(8² + 17²) = √(64 + 289) = √353
The distance between the two points is √353, which is the exact distance in coordinate units.
To sketch the triangle on a coordinate plane, plot the points (1,3) and (9,20), and draw the right triangle by connecting the points and drawing the right angle between the horizontal leg (Δx) and the vertical leg (Δy).