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.
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.