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How to find the Distance, Midpoint, and Slope between two points. Please view this tutorial and answer the follow up questions on paper and turn in to your teacher.

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Distance = The length of a straight line between two points. Midpoint = The point that is halfway between two endpoints on a line segment. Slope = The rate of change of a line.

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The Distance Formula!

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Let’s try an example! Find the distance between points A(3, 5) and B(7, 8). A(3, 5) B(7, 8)

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A(3,5) and B(7,8) First step is to substitute your variables in the correct spot Try putting x 1, y 1 and x 2, y 2 above your points x 1, y 1 x 2, y 2 Remember the order of operations… Simplify the parenthesis first!! Make sure you take the square root!! Square the numbers before you add.

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Let’s try another example! Find the distance between points C(-2, 7) and D(4, 1). C(-2, 7) D(4, 1)

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C(-2, 7) and D(4, 1) Remember to label above your points. x 1, y 1 x 2, y 2 What do you do when you have to subtract a negative? It’s like adding the positive. If the square root is not a whole number, round to at least 2 decimal places

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The Midpoint Formula!

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Let’s try an example! Find the midpoint between points A(3, 5) and B(7, 8). A(3, 5) B(7, 8) Mid Pt(?, ?)

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A(3, 5) and B(7, 8) x 1, y 1 x 2, y 2 Substitute variables in the correct places. Place the labels above the points. Add the numerators before dividing. Remember to keep the answers separated by a comma because they are x and y coordinates of a point.

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Let’s try another example! Find the midpoint between points C(-2, 7) and D(4, 1). C(-2, 7) D(4, 1) Mid pt(?, ?)

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C(-2, 7) and D(4, 1) x 1, y 1 x 2, y 2 Remember to label above the points. What do you do when you have to add a negative? When adding numbers with two different signs, subtract them.

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The Slope Formula!

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Let’s try an example! Find the slope between points A(3, 5) and B(7, 8). A(3, 5) B(7, 8)

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A(3, 5) and B(7,8) x 1, y 1 x 2, y 2 Remember to label. Remember to subtract on the top and bottom first. You can leave the answer in fraction form to see the rise over run.

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Let’s try another example! Find the slope between points C(-2, 7) and D(4, 1). C(-2, 7) D(4, 1)

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C(-2, 7) and D(4,1) x 1, y 1 x 2, y 2 Label!!! Subtracting a negative is just like adding a positive. The fraction can be reduced if it becomes a whole number.

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Follow-Up Questions Answer the following questions on loose leaf and hand them in to your math teacher.

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Follow-Up Questions Find the distance, midpoint and slope for the following sets of points: 1.(2, 5) and (8, 3) 2.(-4, 4) and (5, 7) 3.(0, 9) and (6, 1) 4.(7, -11) and (10, 4) 5.(3, 3) and (8, 8) 6. (21, 16) and (14, 5) 7.(2.4, 3.2) and (5.6, 1.7) 8.(-10, 11.3) and (-3, 7) 9.(34, -2) and (-12, -18) 10.(-5.2, -8.5) and (-6.23, 5.7)

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