Distance and the Pythagorean Theorem Quick Check

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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 5. Data points marked are point A at left parenthesis 1 comma 2 right parenthesis, point B at left parenthesis 3 comma 2 right parenthesis, point C at left parenthesis 3 comma 4 right parenthesis, and point D at left parenthesis 1 comma 4 right parenthesis. A line joins points A to B, B to C, C to D, and D to A, forming a rectangle.

Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.

1 answer

To find the length of the diagonal of the square, we can consider one of the sides of the square as the base of a right triangle.

Let's consider side AB as the base. The length of AB is 3 units.

Now, let's consider the height of the triangle, which is the vertical distance between points A and B. The height is 0 units since the y-coordinates of points A and B are the same.

Using the Pythagorean Theorem, we can find the length of the diagonal of the square:

Diagonal^2 = Base^2 + Height^2
Diagonal^2 = 3^2 + 0^2
Diagonal^2 = 9 + 0
Diagonal^2 = 9
Diagonal = √9
Diagonal = 3 units

Therefore, the length of the diagonal of the square is 3 units.