The coordinate plane below shows point and the line
.
On the coordinate x-y plane, a rectangle has the coordinates at (-2, 3), (5, 3), (-2, -2) and (5, -2).
Which equation describes the line that passes through point P and is perpendicular to the line on the graph?
To find the equation of the line passing through point P (-2, 3) and perpendicular to the given line, we first need to find the slope of the given line.
The given line passes through the points (-2, 3) and (5, -2). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Substitute the coordinates of the given points into the formula to find the slope of the given line:
m = (-2 - 3) / (5 - (-2))
m = -5 / 7 or -5/7
Since the line we are looking for is perpendicular to the given line, the slope of the perpendicular line will be the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is:
m_perpendicular = -1 / m
m_perpendicular = -1 / (-5/7)
m_perpendicular = 7/5 or 1.4
Now we have the slope of the line passing through point P and that is perpendicular to the given line. The equation of the line passing through point P and having a slope of 7/5 is:
y - 3 = 7/5(x + 2)
Simplifying the equation, we get:
y - 3 = 7/5x + 14/5
5y - 15 = 7x + 14
7x - 5y + 29 = 0
Therefore, the equation of the line passing through point P and perpendicular to the given line is 7x - 5y + 29 = 0.