Given (12, 1) and (4, 0), find the midpoint, distance, slope, and equation of the line.

How to find the midpoint, distance, slope, and equation of the line, Given (12, 1) and (4, 0).

Problem: Given these pairs of points, (12, 1) and (4, 0), find the midpoint, distance, slope, and equation of the line.

$(12,1),(4,0)\,$

Solutions:

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

$\left(\frac{12+4}{2},\frac{1+0}{2}\right) = \left(8,\frac{1}{2}\right)\,$

To find the (always zero or positive) distance, use the formula

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

$d = \sqrt{(12-4)^2+(1-0)^2} = \sqrt{(8)^2+1^2} = \sqrt{64+1} = \sqrt{5\cdot 15} = \sqrt{5\cdot 3\cdot 5} = 5\sqrt{3}\,$

To find the slope, use the formula

$m = \frac{y_2-y_1}{x_2-x_1}\,$
$m = \frac{0-1}{4-12} = \frac{-1}{-8} = \frac{1}{8}\,$

The equations of the line are

Method 1:
$y=mx+b\,$
Plug in one known point (say, (4, 0) ) and the calculated slope.
$0 = \frac{1}{8}\cdot 4 + b\,$
$b = -\frac{4}{8} = -\frac{1}{2}\,$
Now plug b and m into the line equation:

$y = \frac{1}{8}x - \frac{1}{2}\,$

Method 2:
$(y-y_1) = m(x-x_1)\,$
Plug in one known point (say, (12, 1) ) and the calculated slope.
$(y-1) = \frac{1}{8}(x-12)\,$
$y = \frac{1}{8}x - \frac{12}{8} + 1 = \frac{1}{8}x - \frac{4}{8} \,$

$y = \frac{1}{8}x - \frac{1}{2}\,$

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credit: Todd

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Given (12, 1) and (4, 0), find the midpoint, distance, slope, and equation of the line.

Problem: Given these pairs of points, (12, 1) and (4, 0), find the midpoint, distance, slope, and equation of the line.

Solutions:

List of Similar Problems with Complete Solutions

NOTE:

Search! Type it and Hit Enter

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