JOURNAL WRITING WARM-UP Bell Quiz 1-7. FROM HERE TO THERE USING THE DISTANCE FORMULA.

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Presentation transcript:

JOURNAL WRITING WARM-UP Bell Quiz 1-7

FROM HERE TO THERE USING THE DISTANCE FORMULA

FROM PYTHAGORAS TO DISTANCE FORMULA We discovered that the Pythagorean theorem works for all right triangles. The square of the hypotenuse of a right triangle, is equal to the sum of the squares of the two adjacent sides

PYTHAGORAS ON THE COORDINATE PLANE Suppose you're given the two points (–2, 1) and (1, 5), and they want you to find out how far apart they are. The points look like this:

YOU CAN DRAW IN THE LINES THAT FORM A RIGHT-ANGLED TRIANGLE, USING THESE POINTS AS TWO OF THE CORNERS: Hypotenuse legs

IT'S EASY TO FIND THE LENGTHS OF THE HORIZONTAL AND VERTICAL SIDES OF THE RIGHT TRIANGLE: JUST SUBTRACT THE X- VALUES AND THE Y-VALUES:

THEN USE THE PYTHAGOREAN THEOREM TO FIND THE LENGTH OF THE THIRD SIDE (WHICH IS THE HYPOTENUSE OF THE RIGHT TRIANGLE): c 2 = a 2 + b 2 This format always holds true. Given two points, you can always plot them, draw the right triangle, and then find the length of the hypotenuse. The length of the hypotenuse is the distance between the two points.

SINCE THIS FORMAT ALWAYS WORKS, IT CAN BE TURNED INTO A FORMULA: Distance Formula: Given the two points (x 1, y 1 ) and (x 2, y 2 ), the distance between these points is given by the formula:

YOUR TURN Find the distance between the points (–2, –3) and (–4, 4). Just plug the coordinates into the Distance Formula: COOL!

The most common mistake made when using the Formula is to accidentally mismatch the x-values and y-values. Be careful you don't subtract an x from a y, or vice versa; make sure you've paired the numbers properly. Also, don't get careless with the square-root symbol. If you get in the habit of omitting the square root and then "remembering" to put it back in when you check your answers in the back of the book, then you'll forget the square root on the test, and you'll miss easy points. You also don't want to be careless with the squaring inside the Formula. Remember that you simplify inside the parentheses before you square, not after, and remember that the square is on everything inside the parentheses, including the minus sign, so the square of a negative is a positive. Things to remember By the way, it is almost always better to leave the answer in "exact" form (the square root). Rounding is usually reserved for the last step of word problems. If you're not sure which format is preferred, do both.

Distance Formula Worksheet HOMEWORK