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Distance Formula
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Distance Formula
A class newspaper team is planning a route between locations on a coordinate grid. Use the distance formula d = √[(x₂ − x₁)² + (y₂ − y₁)²]. Give exact answers when possible; otherwise round to the nearest tenth. Show your calculations.
Build the Route
1.The office is at A(−2, 1) and the print shop is at B(4, 1). Find the distance. What shortcut works because the points have the same y-coordinate?
2.A delivery cart moves from C(3, −4) to D(3, 2). Find the distance and explain why you do not need the full distance formula.
3.Reporter Malik walks from E(−1, −2) to F(3, 1). Find the exact distance and show the changes in x and y.
Solve the Clues
4.Mateo measures between G(−3, 2) and H(1, −1). Which expression correctly gives the distance?
- √[(1 − (−3))² + (−1 − 2)²]
- √[(1 − 3)² + (−1 + 2)²]
- (1 − (−3)) + (−1 − 2)
5.Use your setup from question 4 to find the exact distance between G and H.
6.The newspaper’s map starts at O(0, 0). A newsstand is at P(5, 12). Find the straight-line distance from the origin and write the simplified formula for distance from (0, 0) to any point (a, b).
7.A photographer travels from Q(−2, 4) to R(4, −1). Find the distance to the nearest tenth.
8.For two points with the same x-coordinate, their distance is the absolute difference between their y-coordinates. Decide whether this is true or false, then give a one-sentence reason.
TrueFalse
9.Point S is (2, 1). Point T is (x, 5), and ST = 5 units. Give both possible values of x.
10.Create two coordinate points whose distance is exactly 10 units. Write your points and verify the distance with the formula. One possible answer is acceptable.
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