Question

find the exact distance from the point d(4,-2) to the line segment joining the points e(1,3) and f(-4,-2)

Answer 1

To calculate the exact distance from point D to the line segment EF, one must find the equation of line EF and then use the coordinates of D in the point-to-line distance formula to compute the shortest perpendicular distance.

Step-by-step explanation:

To find the exact distance from point D(4,-2) to the line segment joining points E(1,3) and F(-4,-2), we can use the formula for the distance from a point to a line given in vector form.

The steps to find this distance are:

First, we need to find the equation of the line EF in the form Ax + By + C = 0.

Once we have the equation of the line, we can plug in the coordinates of point D into the distance formula:

d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where (x1,y1) are the coordinates of point D and A, B, and C are the coefficients from the line's equation.

This will give us the perpendicular distance from point D to the line EF, which is the shortest possible distance.