Coordinate Geometry - Mathematics

Explore coordinate geometry fundamentals, including coordinates, gradient, midpoint, distance, and the equation of the line, with a focus on lines and perpendicular lines.

Learn how to find the gradient, or slope, of a line using the formulas y2 - y1 over x2 - x1 and rise over run with coordinates.

Practice finding gradients from lines using the gradient formula with two points. Show that upward lines have positive gradients, like the green line, while downward lines have negative gradients.

Compute midpoints from coordinate pairs using (x1+x2)/2 and (y1+y2)/2. Demonstrate with simple examples like (5,6) and (1,2) yielding (3,4).

Compute the distance between coordinates using the distance formula, as shown for A(4,6) and B(6,10), yielding about 5.65 cm; then apply this distance to find rectangle area.

Apply the distance formula to find distances between coordinate pairs and interpret units like kilometers or centimeters. Practice midpoint and distance problems to master coordinate geometry.

Calculate the gradient from two points and find the y-intercept to form y = mx + c; with (3,9) and (9,2), m = -1.16 and c = 12.48.

Master parallel lines by equal gradients in y = mx + c, and perpendicular lines via m1 m2 = -1, then find intersection points by solving simultaneous equations.

Practice questions reinforce finding the gradient and writing line equations for perpendicular and parallel cases using y = mx + c from given points.