📝 My SAT Math Notes: Circle Diameter Endpoint

When I first started preparing for SAT math, geometry problems like finding endpoints of diameters seemed tricky because many students, including myself, would instinctively try to guess or visually estimate the answer. But through practice, I realized the key is understanding the properties of the circle — specifically, that the center of the circle is exactly the midpoint of the diameter. A quick way to find the other endpoint when given one endpoint and the center is to use the midpoint formula in reverse. Since the center (3, -1) is the midpoint, the coordinates of the other endpoint (x, y) satisfy the equations: (7 + x)/2 = 3 and (2 + y)/2 = -1 Solving these, we get x = -1 and y = -4, which gives the other endpoint as (-1, -4). This approach eliminates guesswork and ensures precise answers — crucial for scoring well on the SAT. Practicing these problems using platforms like MathPath can help identify common traps and reinforce this method. Personally, mastering this concept boosted my confidence with coordinate geometry questions. I recommend writing out the midpoint formula every time you see these problems to avoid errors. Also, visualize the points on a graph if it helps, but rely on calculations for accuracy. Remember, guessing might be tempting, but the exact answer comes from knowing and applying the fundamental rules such as the definition of a circle's center and midpoint formula. This method is not only useful for the SAT but builds a solid foundation for future math studies as well.