Question

Triangles Unit Test
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Question
Use the image to answer the question.

A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9. Data points marked are at left parenthesis 3 comma 2 right parenthesis, and left parenthesis 7 comma 8 right parenthesis. A straight line joins the two points forming a positive slope.

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

Answer 1

To find the length between the two data points (3, 2) and (7, 8), we can compute the differences in the x-coordinates and the y-coordinates and then apply the Pythagorean Theorem.

The difference in the x-coordinates (x2 - x1):
7 (x2) - 3 (x1) = 4

The difference in the y-coordinates (y2 - y1):
8 (y2) - 2 (y1) = 6

Now that we have the differences in both the x and y directions, we can treat these as the lengths of the legs of a right triangle, with the distance between the points as the hypotenuse.

Applying the Pythagorean Theorem (a^2 + b^2 = c^2), where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse:

a^2 = (difference in x)^2 = 4^2 = 16
b^2 = (difference in y)^2 = 6^2 = 36

Now add a^2 and b^2 to get c^2:

c^2 = 16 + 36 = 52

To find c (the length of the hypotenuse/distance between the points), take the square root of 52:

c = √52 ≈ 7.2111

Rounded to the nearest hundredth, the length between the two points is approximately 7.21 units.