Distance on the Coordinate Plane

Key ideas: Distance between two points on the number line (1 dimension) is found by subtracting their coordinates, and using the positive version of the answer (absolute value)

Pythagorean Theorem: a^2+b^2 = c^2  can be used only with right triangles.

Vertical and horizontal lines meet at a right angle (they are perpendicular).

To find the distance between two points on a plane (2 dimensions), it helps to plot them at first.

Connect the points to make a line segment, and then create a right triangle with horizontal and vertical sides.

Find the length of each leg of the right triangle (horizontal leg- x-distance- subtract the x’s; vertical leg- y-distance- subtract the y’s)

Use those lengths in the Pythagorean Theorem to find the hypotenuse, which is the length of the line segment on the coordinate plane.

Eventually, you should see that you don’t really need the diagram. You just subtract the x’s and y‘s for the two lengths, and use them in the Pythagorean Theorem to find the diagonal length on the coordinate plane.

Midpoint

To find the midpoint of two points on the coordinate plane, you find the midpoint of their x values, and the midpoint of their y values. Those two numbers as a coordinate pair are the midpoint. Don’t forget to put your answer in the parenthesis, since they are coordinates.

Remember, to find the midpoint of two numbers, you just add and divide by two (you’re finding their average).

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