Questions

Pythagorean Theorem and Distance Formula

State the term that matches the given description for the first three questions.

1) a mathematical statement that must be proven before it is accepted as being true

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2) a relationship between the three sides of a right triangle such that the sum of the squares of the two legs of the right triangle equals the square of the hypotenuse (the side of the triangle that is opposite the right angle)

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3) In mathematics, the symbol below represents what?

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4) What is the length of the hypotenuse (c)? Label the answer correctly.

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5) What is the length of “a” (leg)? Label the answer correctly.

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6) Find the hypotenuse of the right isosceles triangle that has each congruent side measuring 7 centimeters in length. Label the answer correctly and round to the nearest tenth.

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7) Use the dimensions shown in the picture below to find the height of the building (x). Round the answer to the nearest tenth.

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The development of the distance formula is examined closely in the next three questions. Refer to the figure below to answer the questions. State the letter of the correct answer.

8) The length of segment BC is:

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9) The length of segment CA is:

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10) Use the Pythagorean Theorem to determine the length of “d” in terms of the change in the coordinates. Which statement correctly portrays the development of the distance formula?

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In the next three problems, refer to the figure below and use the distance formula to find the distance between the given points. Each space in the grid represents one unit. Round the answers to the nearest tenth. You may want to print this figure before beginning the exercise. (Right-click on the figure and select “Print Picture”.)

11) What is the distance between points E and B?

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12) What is the distance between points B and D?

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13) What is the distance between points A and F?

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The Midpoint Formulas

State the term that matches the given description for the next two questions.

14) the point that is halfway between two end points of a line segment

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15) In mathematics, the symbol below represents what?

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Refer to the figure below to answer the next three questions.

16) What is the midpoint between points F and B? (Hint: Use the midpoint formula.)

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17) What is the midpoint between points A and D?

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18) What is the midpoint between points K and G?

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Refer to the coordinate system below and use the midpoint formula to solve the next three problems. Each space in the grid represents one unit.

19) State the ordered pair of the midpoint of segment DE.

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20) State the ordered pair of the midpoint of segment EF.

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21) State the ordered pair of the midpoint of segment FG.

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22) In the figure below, point S is the midpoint of segment RT. What are the coordinates of point T?

a.) (7, –1)

b.) (5.5, 0)

c.) (5, 1)

d.) (4, 3)

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