Coordinate Geometry — Distance, Midpoint, Circles

SAT Math · Axiom Academy

Coordinate Geometry: Distance & Midpoint Master the distance formula, midpoint formula, and coordinate geometry applications on the SAT. In this lesson, you'll master: The distance formula and when to use it The midpoint formula for finding the middle of a segment Slope of a line and how to find it from coordinates Equations of circles in coordinate planes The distance formula finds the length of a line segment between two points. This formula comes directly from the Pythagorean theorem! Find the distance between points A(2, 3) and B(5, 7) . (x_1, y_1) = (2, 3) and (x_2, y_2) = (5, 7) The midpoint formula finds the coordinates of the point that is exactly halfway between two points. Find the midpoint of the segment from (1, 4) to (9, 10) . The slope measures how steep a line is. It's the ratio of vertical change to horizontal change. Find the slope of the line through (1, 2) and (4, 8) . Interpretation: For every 1 unit right, the line goes 2 units up. A circle on the coordinate plane can be written as an equation. Write the equation of a circle with center (3, -2) and radius 5. (x - 3)^2 + (y - (-2))^2 = 5^2 (x - 3)^2 + (y + 2)^2 = 25 Find the center and radius of the circle (x + 1)^2 + (y - 4)^2 = 16 . (x - (-1))^2 + (y - 4)^2 = 4^2 Center: (-1, 4) , Radius: 4 What is the distance between (-2, 1) and (2, 4) ? Find the midpoint of the segment from (0, 0) to (6, 8) . Find the center and radius of (x - 2)^2 + (y + 3)^2 = 49 . Distance Formula: (from Pythagorean theorem)

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