Question

Determine the value of a so that the line whose equation is ax - y - 3 = 0 is perpendicular to the line containing the points (2, -2) and (-2, 4).

Options:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4

Answer 1

To determine the value of a such that the line whose equation is ax - y - 3 = 0 is perpendicular to the line containing the points (2, -2) and (-2, 4), the negative reciprocal of the slope of the given line needs to be found. Therefore, the value of a is 2/3.

Step-by-step explanation:

To determine the value of a such that the line whose equation is ax - y - 3 = 0 is perpendicular to the line containing the points (2, -2) and (-2, 4), we need to find the slope of the given line and then find the negative reciprocal of that slope.

The slope of the given line can be found using the formula: m = (y2 - y1) / (x2 - x1)

Using the points (2, -2) and (-2, 4), we have: m = (4 - (-2)) / (-2 - 2) = 6 / -4 = -3/2

The negative reciprocal of -3/2 is 2/3. Therefore, the value of a is 2/3.