Given ΔABC with A(-3, 2), B(-1, -4), and C(4, 1), write the equation for the line containing altitude in standard form. (1 point)
First, we need to find the slope of the given line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of points A and C, the slope of the given line is:
m = (1 - 2) / (4 - (-3)) = -1/7
The slope of a line perpendicular to the given line (which contains the altitude) can be determined by taking the negative reciprocal of the slope of the given line. Therefore, the slope of the line containing the altitude is:
m_perpendicular = -1 / (-1/7) = 7
Now that we have the slope of the line containing the altitude, we can use the formula for the equation of a line in standard form:
Ax + By = C
Substituting the coordinates of point B (-1, -4) into the equation, we can solve for C:
-1 * (-1) + 7 * (-4) = C
1 - 28 = C
C = -27
Therefore, the equation of the line containing the altitude is:
7x - y = -27