Questions: The slope of the line passing through points (x1, y1) and (x2, y2) is found using the formula (y2-y1)/(x2-x1). The line passing through the points (1,2) and (x, 5) is perpendicular to a line that has a slope of 1/3. What is the value of x ? A 10 B -2 C -4 D 0

Solution Steps

To find the value of \( x \), we need to determine the slope of the line passing through the points \((1, 2)\) and \((x, 5)\). Since this line is perpendicular to a line with a slope of \(\frac{1}{3}\), its slope must be the negative reciprocal, which is \(-3\). We set up the equation for the slope \(\frac{5 - 2}{x - 1} = -3\) and solve for \( x \).

The line passing through the points \((1, 2)\) and \((x, 5)\) is perpendicular to a line with a slope of \(\frac{1}{3}\). Therefore, the slope of our line must be the negative reciprocal of \(\frac{1}{3}\), which is \(-3\).

The slope of the line through the points \((1, 2)\) and \((x, 5)\) is given by the formula: \[ \frac{5 - 2}{x - 1} = -3 \]

Simplify and solve the equation: \[ \frac{3}{x - 1} = -3 \] Multiply both sides by \((x - 1)\) to eliminate the fraction: \[ 3 = -3(x - 1) \] Distribute the \(-3\): \[ 3 = -3x + 3 \] Subtract 3 from both sides: \[ 0 = -3x \] Divide by \(-3\): \[ x = 0 \]

Final Answer