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?
A.
B.
C.
D.
To find the equation of the line passing through point P that is 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 the given line is (change in y) / (change in x) = (-2 - 3) / (5 - (-2)) = -5 / 7.
Since the line we want is perpendicular to this line, its slope will be the negative reciprocal of -5 / 7, which is 7 / 5.
Now, we have the slope (m) of the line passing through point P. We also have the coordinates of point P, which is (x, y) = (-2, 3).
Using the point-slope form of the equation of a line, the equation of the line passing through point P that is perpendicular to the given line is:
y - 3 = (7/5)(x - (-2))
y - 3 = (7/5)(x + 2)
Multiplying through by 5 to clear the fraction:
5(y - 3) = 7(x + 2)
5y - 15 = 7x + 14
Rearranging in standard form:
7x - 5y = -29
Therefore, the correct answer is:
D. 7x - 5y = -29