Question

Please help!!!!!!!!!!!!!!

Answer 1

Answer:   7.1

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Explanation:

The two points are (x1,y1) = (1,3) and (x2,y2) = (8,4)

Use the distance formula to get,

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (3-4)^2}\\\\d = \sqrt{(-7)^2 + (-1)^2}\\\\d = \sqrt{49 + 1}\\\\d = \sqrt{50}\\\\d = \sqrt{25*2}\\\\d = \sqrt{25}*\sqrt{2}\\\\d = 5\sqrt{2}\\\\d \approx 7.0710678\\\\d \approx 7.1$

Alternatively, you can plot the two points A(1,3) and B(8,4) on the same xy grid. Then plot point C(8,3). Note that C has the same x coordinate as B, and the same y coordinate as A. Triangle ABC is a right triangle, where the 90 degree angle is at point C. The distance from A to B is the same as finding the length of AB, which is the hypotenuse.

This means we can apply the pythagorean theorem to find the hypotenuse AB. The distance formula is a modified version of the pythagorean theorem. Refer to the diagram below.