High School Geometry - All Formulas (Detwiler)

Midpoint Formula

Given points a and b on a number line.

•  $M\left(\frac{a+b}{2}\right)$  

•  $M\left(\frac{a-b}{2}\right)$  

•  $M\left(a,b\right)$  

•  $M\left(\frac{b-a}{2}\right)$  

Tags

CCSS.HSG.GPE.B.6

Midpoint Formula
On a plane with endpoints  $\left(x_1,\ y_1\right)$  and  $\left(x_2,\ y_2\right)$  .

•  $d=\sqrt{\left(\left(x_2-\ x_1\right)^2+\left(y_2-\ y_1\right)^2\right)}$  

•  $M\left(x_2-\ x_1,\ y_2-\ y_1\right)$  

•  $M\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)$  

•  $M\left(\frac{x_1-x_2}{2},\ \frac{y_1-y_2}{2}\right)$  

Tags

CCSS.HSG.CO.D.12

CCSS.HSG.GPE.B.6

Distance Formula
On a plane with endpoints $\left(x_2,\ y_2\right)$  and  $\left(x_2,\ y_2\right)$ .

•  $d=\sqrt{\left(x_1-y_1\right)^2+\left(x_2-y_2\right)^2}$  

•  $d=\sqrt{\left(x_2-y_1\right)^2+\left(x_1-y_2\right)^2}$  

•  $d=\sqrt{\left(x_2+x_1\right)^2-\left(y_2+y_1\right)^2}$  

•  $d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$  

Tags

CCSS.HSG.GPE.B.7

Perimeter of a Square

• $P=4s$

• $P=s^2$

• $P=a+b+c$

• $P=s$

Tags

CCSS.HSA.CED.A.4

CCSS.HSA.SSE.B.3

CCSS.HSG.MG.A.1

Area of a Square

• $A=4s$

• $A=s^2$

• $A=\frac{1}{2}bh$

• $A=\frac{1}{2}h\left(b_1+b_2\right)$

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.MG.A.1

Perimeter of a Rectangle

• $P=4s$

• $P=s^2$

• $P=2b+2h$

• $P=bh$

Tags

CCSS.HSG.GPE.B.7

CCSS.HSG.MG.A.1

Area of a Rectangle

•  $A=4s$ 

•  $A=s^2$ 

•  $A=2b+2h$ 

•  $A=bh$ 

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GPE.B.7

Perimeter of a Triangle

• $P=4s$

•  $P=a+b+c$ 

•  $P=\frac{1}{2}bh$ 

• $P=s$

Tags

CCSS.HSG.GPE.B.7

Area of a Triangle

• $A=4s$

•  $A=bh$ 

• $A=\frac{1}{2}bh$

• $A=\frac{1}{2}h\left(b_1+b_2\right)$

Tags

CCSS.HSG.GPE.B.7

CCSS.HSG.SRT.D.9

Circumference of a Circle

• $C=d\pi$

• $C=\pi r^2$

• $C=2\pi r$

• $C=2\pi r^2$

Tags

CCSS.HSG.GMD.A.1