Distance and the Pythagorean Theorem Practice

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A map shows a grid 17 units across and 12 units high, superimposed over shapes that represent streets and buildings. A key lists buildings located in Washington D.C. that correspond to points on the grid. Point A represents the White House. It is located at 4 units across from the left, and 3 units down from the top. Point B represents the Washington Monument, located at 5 units across and 9 units down. Point C represents the Natural History Museum, and is located at approximately 8 units across and 8 units down. Point D represents the Smithsonian, and is located at 10 units across and 10 units down. Point E represents the National Portrait Gallery, and is located at 12 units across and 3 units down. Point F represents the National Gallery of Art, and is located at 14 units across and 8 units down. A scale shows 200 feet and 200 meters.

Find the length between landmark A
and landmark E
.

(1 point)

Answer 1

To find the distance between points A (4, 3) and E (12, 3) on the grid, we can use the distance formula derived from the Pythagorean theorem:

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

Where:

• \((x_1, y_1)\) are the coordinates of point A
• \((x_2, y_2)\) are the coordinates of point E

Substituting the coordinates of A and E into the formula:

• A (4, 3) gives us \(x_1 = 4\) and \(y_1 = 3\)
• E (12, 3) gives us \(x_2 = 12\) and \(y_2 = 3\)

Now plug in the values:

\[ d = \sqrt{(12 - 4)^2 + (3 - 3)^2} \] \[ d = \sqrt{(8)^2 + (0)^2} \] \[ d = \sqrt{64 + 0} \] \[ d = \sqrt{64} \] \[ d = 8 \]

So, the distance between landmark A and landmark E is 8 units.