Final answer:
To find the coordinates of point N that divides the segment LM into two equal parts, we average the coordinates of L and M to get N's coordinates (-3.5, 4), with the product being -14.
Step-by-step explanation:
The question asks us to find the coordinates of point N which divides the line segment LM in a ratio of 1:1. Since this is a midpoint division, we can find the coordinates of N by averaging the x-coordinates and the y-coordinates of points L and M.
Coordinates of L (-8, 7) and M (1, 1)The x-coordinate of N is (-8 + 1)/2 = -7/2 or -3.5. The y-coordinate of N is (7 + 1)/2 = 8/2 or 4.Therefore, the coordinates of N are (-3.5, 4). The product of the coordinates of N is -3.5 * 4 = -14.Write the final answer in 20 words: The coordinates of point N are (-3.5, 4), and the product of these coordinates is -14.To find the coordinates of point N, we need to find the midpoint of LM. The midpoint formula is (x1 + x2)/2, (y1 + y2)/2. So, the x-coordinate of N is (-8 + 1)/2 = -7/2 and the y-coordinate of N is (7 + 1)/2 = 8/2 = 4. Therefore, the coordinates of N are (-7/2, 4).To find the product of the coordinates of N, we multiply the x-coordinate and the y-coordinate: (-7/2) * 4 = -14/2 = -7.