Question

Determine the shortest distance from the point H(-4, -9) to the line through points J(-10,9) and K(-5,-6).

a) 13 units
b) 15 units
c) 17 units
d) 19 units

Answer 1

To find the shortest distance from point H to the line through points J and K, one must derive the equation of the line, then use the point-to-line distance formula.

Step-by-step explanation:

The question asks to determine the shortest distance from a point to a line in a 2D coordinate system. To find the shortest distance from a point to a line, one can use the formula d = |Ax1 + By1 + C| / √(A² + B²), where d is the distance, (x1, y1) are the coordinates of the point, and A, B, and C are the coefficients of the line's equation in the form Ax + By + C = 0.

First, we need to find the equation of the line that passes through points J and K. Using the two-point form of a line's equation, we can derive the slope and then the full equation. Once we have the equation, we can plug in the coordinates of point H along with the coefficients into the distance formula to find the distance.

The shortest distance in this specific case will be one of the given options ${(a) – (d)}; we will calculate the exact value through the steps mentioned.