Quick Answer
The Distance Formula is a coordinate geometry tool used on the Digital SAT to find the length between two points (x1, y1) and (x2, y2). It appears frequently in Math Modules 1 and 2, typically within Geometry or Problem Solving questions. Students often use it to solve for side lengths or circle radii.
The Distance Formula, d = √[(x₂ - x₁)² + (y₂ - y₁)²], calculates the straight-line distance between two points on a Cartesian coordinate plane. It is derived from the Pythagorean Theorem, where the distance represents the hypotenuse of a right triangle.
Question: What is the distance between point A(2, -3) and point B(5, 1) in the xy-plane? Solution: Using the formula d = √[(5 - 2)² + (1 - (-3))²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Sign Errors: Students frequently forget that subtracting a negative coordinate results in addition, such as calculating 1 - (-3) incorrectly.
Incorrect Squaring: Forgetting that any real number squared, including negative differences, must result in a positive value before adding.
Formula Confusion: Mixing up the Distance Formula with the Midpoint Formula by adding coordinates instead of subtracting them before squaring.
Students targeting 750+ should know that the Distance Formula is simply the Pythagorean Theorem in disguise; recognizing this allows you to quickly sketch a right triangle on the coordinate plane and use 3-4-5 or 5-12-13 Pythagorean triples to solve distance problems without performing the full calculation.
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