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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

To find the length of the diagonal of the rectangle formed by the points \((-6, 8)\), \( (4, 8)\), \( (4, -3)\), and \((-6, -3)\), we can use the Pythagorean theorem.

The length of the diagonal can be calculated using the coordinates of two opposite corners of the rectangle. In this case, we can use the points \((-6, 8)\) and \( (4, -3)\).

The diagonal \(d\) can be calculated using the formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting in the coordinates of the points:

\[ (x_1, y_1) = (-6, 8) \quad \text{and} \quad (x_2, y_2) = (4, -3) \]

Now we calculate:

\[ d = \sqrt{(4 - (-6))^2 + (-3 - 8)^2} \]

This simplifies to:

\[ d = \sqrt{(4 + 6)^2 + (-11)^2} \] \[ d = \sqrt{10^2 + (-11)^2} \] \[ d = \sqrt{100 + 121} \] \[ d = \sqrt{221} \]

Now, approximate \(\sqrt{221}\):

\[ \sqrt{221} \approx 14.87 \]

So, the length of the diagonal of the rectangle is approximately \(14.87\) units.

Thus, your answer is:

14.87 units