Difference between revisions of "Alg6.2"

From Example Problems
Jump to navigation Jump to search
 
(One intermediate revision by the same user not shown)
Line 9: Line 9:
 
To find the (always zero or positive) distance, use the formula <math>d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,</math><br><br>
 
To find the (always zero or positive) distance, use the formula <math>d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,</math><br><br>
  
<math>d = \sqrt{(12-4)^2+(1-0)^2} = \sqrt{(8)^2+1^2} = \sqrt{64+1} = \sqrt{5*15} = \sqrt{5*3*5} = 5\sqrt{3}\,</math><br><br>
+
<math>d = \sqrt{(12-4)^2+(1-0)^2} = \sqrt{(8)^2+1^2} = \sqrt{64+1} = \sqrt{5\cdot 15} = \sqrt{5\cdot 3\cdot 5} = 5\sqrt{3}\,</math><br><br>
  
 
To find the slope, use the formula <math>m = \frac{y_2-y_1}{x_2-x_1}\,</math><br><br>
 
To find the slope, use the formula <math>m = \frac{y_2-y_1}{x_2-x_1}\,</math><br><br>
Line 17: Line 17:
 
The equations of the line are<br><br>
 
The equations of the line are<br><br>
  
<b>Form 1:</b> <math>y=mx+b\,</math><br><br>\n\nPlug in one known point (say, <math>(4,0)\,</math>) and the calculated slope.<br><br>
+
<b>Form 1:</b> <math>y=mx+b\,</math><br><br>
  
<math>0 = \frac{1}{8}\cdot 4 + b\,</math><br><br>\n\n<math>b = -\frac{4}{8} = -\frac{1}{2}\,</math><br><br>
+
Plug in one known point (say, <math>(4,0)\,</math>) and the calculated slope.<br><br>
 +
 
 +
<math>0 = \frac{1}{8}\cdot 4 + b\,</math><br><br>
 +
 
 +
<math>b = -\frac{4}{8} = -\frac{1}{2}\,</math><br><br>
  
 
Now plug <math>b</math> and <math>m</math> into the line equation:<br><br>
 
Now plug <math>b</math> and <math>m</math> into the line equation:<br><br>

Latest revision as of 22:16, 7 November 2005

For these pairs of points, find the midpoint, distance, slope, and equation of the line.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (12,1),(4,0)\,}

To find the midpoint, average the x coordinates and y coordinates. The midpoint is

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\frac{12+4}{2},\frac{1+0}{2}\right) = \left(8,\frac{1}{2}\right)\,}

To find the (always zero or positive) distance, use the formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d = \sqrt{(12-4)^2+(1-0)^2} = \sqrt{(8)^2+1^2} = \sqrt{64+1} = \sqrt{5\cdot 15} = \sqrt{5\cdot 3\cdot 5} = 5\sqrt{3}\,}

To find the slope, use the formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m = \frac{y_2-y_1}{x_2-x_1}\,}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m = \frac{0-1}{4-12} = \frac{-1}{-8} = \frac{1}{8}\,}

The equations of the line are

Form 1: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=mx+b\,}

Plug in one known point (say, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (4,0)\,} ) and the calculated slope.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 = \frac{1}{8}\cdot 4 + b\,}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b = -\frac{4}{8} = -\frac{1}{2}\,}

Now plug Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} into the line equation:

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \frac{1}{8}x - \frac{1}{2}\,}

Form 2: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y-y_1) = m(x-x_1)\,}

Plug in one known point (say, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (12,1)\,} ) and the calculated slope.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y-1) = \frac{1}{8}(x-12)\,}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \frac{1}{8}x - \frac{12}{8} + 1 = \frac{1}{8}x - \frac{4}{8} \,}

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \frac{1}{8}x - \frac{1}{2}\,}

Main Page : Geometry