# Formula Chart for Geometry on the SBAC Test

Geometry is literally everywhere! It’s in the shape of the stars and planets, in the food you eat, in your smartphone, and even in the icons for the apps in your smartphone. All the different shapes in the universe can be described by formulas and equations, and for Geometry on the SBAC Test, you need to know how to handle those formulas. The following chart is intended for study purposes only, as you won’t be able to use it during the actual test, but is really helpful to learn how to handle them when solving Geometry problems on the SBAC Test!

You can find free practice for the SBAC at Union Test Prep.

And you can find our other four formula charts for this test here:

Algebra

Functions

Number and Operations

Statistics and Probability

## Geometry Formulas for the SBAC

Category Formula Symbols Comment
Transformations $$(x,y)\rightarrow(x, -y)$$ Reflection x-axis
Transformations $$(x,y)\rightarrow(-x, y)$$ Reflection y-axis
Transformations $$(x,y)\rightarrow(-x, -y)$$ Reflection Origin
Transformations $$(x,y)\rightarrow(y, x)$$ Reflection line y = x
Transformations $$(x,y)\rightarrow(-y, -x)$$ Reflection line y = -x
Transformations $$(x,y)\rightarrow(y, -x)$$ Rotation $$90^o$$ Counterclockwise
Transformations $$(x,y)\rightarrow(-x, -y)$$ Rotation $$180^o$$ Counterclockwise
Transformations $$(x,y)\rightarrow(x+a, y+b)$$ Translation
Transformations $$(x,y)\rightarrow(rx, ry)$$ Dilation (r = scale factor)
Right Triangles $$a^2+b^2=c^2$$ a, b = legs of a right triangle
c = hypotenuse of a right triangle
Pythagorean
Theorem
Coordinates $$y = m \cdot x + b$$ y = dependent variable
m = slope
x = independent variable
b = y-axis intercept
Slope-Intercept Form
of a line: Try to
convert any given linear
equation to this form.
Coordinates $$m= \frac{(y_2-y_1)}{(x_2-x_1)}$$ $$m$$ = slope
$$y_n$$ = dependent variable at point n
$$x_n$$ = independent variable at point n
This is a rearranged
version of the
point-slope form.
Coordinates $$y-y_1=m(x-x_1)$$ $$(x_1, y_1)$$ = point on the line
y = dependent variable
x = independent variable
m = slope
Point-slope form
of a line
Coordinates $$d=\sqrt{(y_2-y_1)^2 +(x_2-x_1)^2}$$ d = distance between two points
$$y_n$$ = y value at point n
$$x_n$$ = x value at point n

Coordinates $$(x_m, y_m) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$$ $$x_m$$ = x value at the midpoint
$$y_m$$ = y value at the midpoint
$$y_n$$ = y value at point n
$$x_n$$ = x value at point n

Volume $$V=l \cdot w \cdot h$$ V = volume of rectangular prism
l = length
w = width
h = height

Volume $$V = \frac{1}{3} \cdot l \cdot w \cdot h$$ V = volume of pyramid
l = length
w = width
h = height

Volume $$V = \pi \cdot r^2 \cdot h$$ V = volume of a cylinder
r = radius
h = height

Volume $$V= \frac{4}{3} \cdot \pi \cdot r^3$$ V = volume of a sphere
r = radius

Circles $$C = 2 \cdot \pi \cdot r$$
$$C = \pi \cdot d$$
C = circumference (perimeter)
r = radius
d = diameter
$$\pi$$ = 3.14

Circles $$s = r \cdot \theta$$ s = arc length
r = radius
$$\theta$$ = central angle (radians

Circles $$A = \pi \cdot r^2$$ A = area of a circle
r = radius

Conic Sections $$(x-h)^2 + (y-k)^2 = r^2$$ $$(h, k)$$ = center of circle
r = radius
Standard form of
a circle
Conic Sections $$(x-h)^2 = 4p \cdot (y-k)$$ $$(h, k)$$ = vertex of a parabola
p = distance from vertex to directrix
Parabola that opens
up or down
Conic Sections $$(y-k)^2 = 4p \cdot (x-h)$$ $$(h, k)$$ = vertex of a parabola
p = distance from vertex to directrix
Parabola that opens
left or right
Shapes $$A=\frac{1}{2} \cdot b \cdot h$$ A = area of a triangle
b = base
h = height

Shapes $$A = s^2$$ A = area of a square
s = side length

Shapes $$A=l \cdot w$$ A = area of a rectangle
l = length
w = width

Shapes $$A=h \cdot \frac{(b_1+b_2)}{2}$$ A = area of a trapezoid
$$b_n$$ = base n
h = height

## Trigonometry

$sin\ \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac {1}{ csc\ \theta}$ $cos\ \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac {1}{ sec\ \theta}$ $tan\ \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac {1}{ cot\ \theta}$