Distance Between Two Points (Leaving Cert Mathematics): Quizzes

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Distance Between Two Points
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What does the distance formula calculate between two points?

The straight-line distance

What is the distance formula for points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)?

(x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Which theorem is the distance formula derived from?

Pythagorean theorem

What is the length of the horizontal leg when connecting two points?

∣x2−x1∣|x_2 - x_1|

What is the final step in the five-step distance calculation process?

Take the square root

What is the distance between points A(3, 5) and B(8, 2)?

34\sqrt{34}

For A(3, 5) and B(8, 2), what is (x2−x1)2+(y2−y1)2(x_2 - x_1)^2 + (y_2 - y_1)^2?

34

What does 'equidistant' mean?

Same distance from both points

What is the distance from D(2, 4) to E(-5, 1)?

58\sqrt{58}

If distance between (2, 3) and (5, k) is 10\sqrt{10}, what are the possible values of k?

k = 2 or k = 4

What is the value of (−3)2(-3)^2?

9

Which is a key application of the distance formula?

Proving triangles are isosceles

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