Question

leo drew a line that is perpendicular to the line shown on the grid and passes through point (f, g). which of the following is the equation of leos line?

\\(y - g = -2(x - f)\\)

\\(y + f = 2(x + g)\\)

\\(y + f = \frac{1}{2}(x + g)\\)

\\(y - g = \frac{1}{2}(x - f)\\)

Explanation:

Find the slope of the given line

The line passes through the grid intersections \((0, 3)\) and \((1, 1)\).

$$ m_1 = \frac{1 - 3}{1 - 0} = -2 $$

Determine the perpendicular slope

The slope of a line perpendicular to a line with slope \(m_1 = -2\) is the negative reciprocal.

$$ m_2 = -\frac{1}{m_1} = \frac{1}{2} $$

Write the equation in point-slope form

Using the point \((F, G)\) and slope \(m_2 = \frac{1}{2}\):

$$ y - G = \frac{1}{2}(x - F) $$

Answer:

• \(y - G = -2(x - F)\)
• \(y + F = 2(x + G)\)
• \(y + F = \frac{1}{2}(x + G)\)
• \(y - G = \frac{1}{2}(x - F)\) (Correct answer)