Find the distance from point (-1, 3) to the line 5x- 4y= 10.
To find the distance from a point to a line, we can use the formula:
Distance = |Ax + By + C| / √(A^2 + B^2)
where (x, y) is a point on the line and (A, B, C) are the coefficients of the equation of the line.
In this case, the equation of the line is 5x - 4y = 10, which can be rewritten in the form Ax + By + C = 0 as -5x + 4y - 10 = 0.
Now, let's substitute the coordinates of the given point (-1, 3) into the distance formula:
Distance = |(-5)(-1) + (4)(3) - 10| / √((-5)^2 + 4^2)
Simplifying:
Distance = |5 + 12 - 10| / √(25 + 16)
Distance = |7| / √41
Finally, the distance from the point (-1, 3) to the line 5x - 4y = 10 is 7 / √41 (approximately 1.09 units).