Find the distance between P(-4,3) and the line with equation: 2x - 5y = -7
a. (14√29)/29
b. 0
c. (-16√29)/29
d. (16√29)/29
I got C but would it be positive, like D?
You are finding distance, so it would be the absolute value, namely D
Are you using the method
for a point (p,q) to the line Ax + By + C = 0
distance = │Ap + Bq + C│/√(A^2+B^2) ?
oh okay, thought so
thanks!
To find the distance between a point and a line, we can use the formula:
distance = |Ax + By - C| / sqrt(A^2 + B^2)
Given that the equation of the line is 2x - 5y = -7, we can rewrite it in the form Ax + By - C = 0:
2x - 5y + 7 = 0
Comparing the equation of the line with the general form Ax + By - C = 0, we have A = 2, B = -5, and C = -7.
Now, let's substitute the coordinates of the point P(-4,3) into the formula:
distance = |2*(-4) + (-5)*(3) - (-7)| / sqrt(2^2 + (-5)^2)
distance = |-8 - 15 + 7| / sqrt(4 + 25)
distance = |-16| / sqrt(29)
distance = 16 / sqrt(29)
Therefore, the correct answer is option D: (16√29)/29.
Note: The distance is always positive because it represents the magnitude of the distance between the point and the line.
To find the distance between a point and a line, you can use the formula for the distance from a point to a line. In this case, we have the point P(-4, 3) and the line with equation 2x - 5y = -7.
The formula for the distance from a point (x1, y1) to a line Ax + By + C = 0 is:
distance = |Ax1 + By1 + C| / √(A^2 + B^2)
Let's apply this formula to find the distance.
Given:
Point P: (-4, 3)
Line equation: 2x - 5y = -7
First, let's rearrange the line equation to the standard form:
2x - 5y + 7 = 0
By comparing it with the general form (Ax + By + C = 0), we can determine the values of A, B, and C:
A = 2
B = -5
C = 7
Now, substitute these values into the distance formula:
distance = |2(-4) - 5(3) + 7| / √(2^2 + (-5)^2)
distance = |-8 - 15 + 7| / √(4 + 25)
distance = |-16| / √(29)
distance = 16 / √(29)
Therefore, the distance between point P and the line is (16√29)/29.
So, the correct answer is (d) (16√29)/29 and not (c) (-16√29)/29.
The answer is positive because distance is a scalar quantity and represents the magnitude or absolute value of the distance. Hence, we do not consider the negative sign.