Algebra 2 Distances

Question

Find the distance between (2,-6) and (7,4)

Answer 1

Think of the points as corners in a right triangle like this:

To find "c", just use the Pythagorean Theorem a² + b² = c² or c = √(a² + b²)

a = the difference in the x-values of the points: 7 - 2 = 5

b = the difference in the y-values of the points: 4 - -6 = 10

c = √(5² + 10²) = √(25 + 100) = √125 = √25•5 = 5√5 (or, plugging it into a calculator) ≈ 11.18 (but use 5√5 as your answer)

Answer 2

This uses the distance formula, which has 5 steps, which must be done in the correct order. First I will write out the formula: distance =

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√ (x2 - x1)² + (y2 - y1)²

Point 1 (2, -6) so x1 = 2 and y1 = -6

Point 2 (7,4) so x2 = 7 and y2 = 4

Step 1; x2 - x1 = 7 - 2 = 5

Step 2: y2 - y1 = 4 - (-6) = 4 + 6 = 10

Step 3: SQUARE both of your answers from Steps 1 and 2 5²=25 10² = 100

Step 4: ADD these two results together 25 + 100 = 125

Step 5: SQUARE ROOT the result from step 4 √125 = 5√5 for the exact answer

≈ 11.18 is the approximate answer