Geometry End of Year

Prove that a figure is a paralleogram
How to find out if two lines are parallel

Geometric Formulas Reference

  1. Parabola Formulas:

    • General Equation: (x−h)2+(y−k)2=(y−d)2(x-h)^2 + (y-k)^2 = (y-d)^2

    • Standard Form (Vertical): (x−h)2=4p(y−k)(x-h)^2 = 4p(y-k)

    • Standard Form (Horizontal): (y−k)2=4p(x−h)(y-k)^2 = 4p(x-h)

  2. Distance and Midpoint:

    • Distance Formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

    • Midpoint Formula: M=(x1+x22,y1+y22)M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})

  3. Linear Equation Forms:

    • Standard Form: Ax+By=CAx + By = C

    • Slope-Intercept Form: y=mx+by = mx + b

    • Point-Slope Form: y−y1=m(x−x1)y - y_1 = m(x - x_1)

  4. Circle Formulas:

    • Standard Form: (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2

B. To divide Standard Form to get into Slope-Intercept form you have to divide X / Y

C.

Testing Points

To check if a point (x,y) is on a parabola, you must substitute both coordinates into the general equation (x−h)2+(y−k)2=(y−d)2(x-h)^2 + (y-k)^2 = (y-d)^2 and see if the equation is true.