Alg6.4

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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 (-5,15),(-5,9)\,}

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{-5-5}{2},\frac{15+9}{2}\right) = \left(-5,\frac{15+9}{2}\right) = \left(-5,\frac{15+9}{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{(-5+5)^2+(15-9)^2} = \sqrt{0^2+6^2} = \sqrt{6^2} = 6\,}

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{9-15}{-5-(-5)} = undefined\,} (which means it is a vertical line, which has infinite slope)

Since the line is vertical, there is only one x value that will give all y values. The equation for the line 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 x = -5\,}

Algebra

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