Question

Distance and the Pythagorean Theorem Practice

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Question
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A graph shows four quadrants with the x-axis and y-axis both ranging from negative 10 to positive 10 in increments of 1. Unlabeled points are plotted at left parenthesis negative 6 comma 8 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 4 comma negative 3 right parenthesis, and left parenthesis negative 6 comma negative 3 right parenthesis. A straight line joins the four points forming a rectangle.

What is the length of the diagonal of the rectangle? Round your answer to the nearest hundredth, if necessary.

(1 point)
units

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the diagonal of the rectangle, we can use the distance formula. The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we have a rectangle, which can be split into two right triangles. The length of the diagonal is the hypotenuse of one of these right triangles.

Let's label the points as follows:
A: (-6, 8)
B: (4, 8)
C: (4, -3)
D: (-6, -3)

To find the length of the diagonal, we need to find the distance between points A and C.

Using the distance formula:

d(A, C) = √((xC - xA)^2 + (yC - yA)^2)

Substituting the values:

d(A, C) = √((-6 - 4)^2 + (8 - (-3))^2)
= √((-10)^2 + (8 + 3)^2)
= √(100 + 11^2)
= √(100 + 121)
= √221

Rounding to the nearest hundredth, the length of the diagonal is approximately 14.87 units.