Determine the distance from the point 𝑃 (4,3) to the line with equation 3𝑥 − 4𝑦 + 25 = 0.
distance from a point (p,q) to a line Ax + By + C = 0
= |Ap + Bq + C| / √(A^2 + B^2)
plug in your values
To determine the distance from a point to a line, we can use the formula for the distance between a point and a line. The formula is given by:
distance = |Ax + By + C| / sqrt(A^2 + B^2)
Where A, B, and C are the coefficients of the line equation, and (x, y) are the coordinates of the point.
In this case, we have the line equation as 3𝑥 − 4𝑦 + 25 = 0, so A = 3, B = -4, and C = 25.
We also have the point P(4,3), so x = 4, and y = 3.
Now, let's substitute these values into the formula and calculate the distance:
distance = |3*4 + (-4)*3 + 25| / sqrt(3^2 + (-4)^2)
distance = |12 - 12 + 25| / sqrt(9 + 16)
distance = |25| / sqrt(25)
distance = 25 / 5
distance = 5
Therefore, the distance from the point P(4,3) to the line 3𝑥 − 4𝑦 + 25 = 0 is 5 units.