ACT-Style: Midpoint and Distance Applications

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Midpoint and Distance Applications Two cities, one road each to the midpoint — combining the midpoint and distance formulas in a single real-world ACT question Two cities are represented on a coordinate grid, with distances measured in miles. City A is located at (10, 15) and City B is located at (40, 35) . A road is built from each city straight to the midpoint between them. What is the distance, in miles, that City A must build to reach the midpoint? Round to the nearest mile. Nice work — you combined two formulas in one ACT question, which is exactly how the test likes to test coordinate geometry. Midpoint first: — average the x 's, average the y 's. Forgetting to divide by 2 is the single most common slip. Then distance: applies to ANY two points — including a city and a midpoint you just found. Free geometry fact: a midpoint is equidistant from both endpoints, so City B's road is also miles — the ACT sometimes asks for that distance too, hoping you'll redo work you already have. Multi-step coordinate geometry questions on the ACT almost always chain two formulas together — spot which one comes first before you touch a calculator.

This is the written version of the interactive lesson above. See the full ACT Math course.