The answer will be the diagonal (hypotenuse) for a horizontal distance x2-x1 (-6) and a vertical distance y2-y1 (8). The square root of the squares is sqrt [62 + 82] = sqrt [100] = 10.
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The distance between points can be calculated using Pythagoras: distance = √(change_in_x² + change_in_y²) → distance = √((4 - 10)² + (36 - 12)²) → distance = √((-6)² + (24)²) → distance = √(36 + 576) → distance = √612 → distance = 6 √17 ≈ 24.74 units.
The distance along a straight line is 10. Using the Pythagorean equation, c2 = a2 + b2 where the x change is 6 and the y change is 8, c2 = 62 + 82 = 36 + 64 = 100 c = [sqrt 100] = 10
We use the distance formula to find the distance between the points (2,3) and (3,0) The distance is Square root of ((3^2+(2-3)^2)= Square root of (9+1) Which is square root of 10. This is the distance. This works because if we draw a triangle with one side having length 3 and another side having length 1, we have a right triangle. THis is because the side of length 3 is vertical and the side of length 1 is horizontal. Now the hypotenuse of this triangle is the line between the two points in question. So the length of the hypotenuse is the distance between the points. However, the pythagorean theorem tells us this distance is the square root of 1^2 +3^2=Square root of 10
The Pythagorean distance is sqrt[(4 - 7)2 + (7 - 8)2] = sqrt[9 + 1] = sqrt(10) = 3.162 approx.