Final answer:
To find the coordinates of point L, we calculate the slope of line JK, which is -19/17, and then use the negative reciprocal for the slope of JL, which is 17/19. By moving along this slope from point J, we find that L(9, 27) is the point that makes JL perpendicular to JK.
Step-by-step explanation:
To determine the coordinates of point L so that line JL is perpendicular to line JK, we first need to find the slope of line JK and then use the negative reciprocal of that slope for line JL, because perpendicular lines have slopes that are negative reciprocals of each other. Calculating the slope of JK using the points J(-10, 10) and K(7, -9):
- Slope of JK = (y2 - y1) / (x2 - x1) = (-9 - 10) / (7 - (-10)) = -19 / 17.
- The slope of JL must be the negative reciprocal of -19/17, which is 17/19.
Now, we need a point L that is on the line JL with this slope. Starting at point J (-10, 10), we can move according to the slope 17/19 to find a coordinate for L that should be a whole number. If we move 19 units in the x-direction (to make the calculations simpler), the corresponding change in the y-direction should be 17 units.
- L's x-coordinate: -10 + 19 = 9
- L's y-coordinate: 10 + 17 = 27
Therefore, L's coordinates are (9, 27), which corresponds to answer option D. L(9, 27).