A ship at one point and a port at another: how far apart are they? Where is the point halfway between them? Here we find the distance between two points, the midpoint, the point that divides a line in a ratio, and we use them to study shapes.
3 lessons, about 1 h 15 min3 simulations10 problems6 practice questionsPython in every lesson
Created by StemPy LabThe distance between two points comes from the Pythagoras theorem: square the horizontal and vertical steps, add them, and take the square root. From the origin it is the square root of x squared plus y squared.
A point that divides AB in the ratio m to n is found with the section formula, a weighted average of the two ends. Equal weights give the midpoint, and the ratios 1 to 2 and 2 to 1 give the points of trisection.
Name a triangle by comparing the squares of its sides. The area of a triangle comes from its three corners, and it is zero when the points are collinear. The centroid is the average of the corners.
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