Final answer:
The coordinates of midpoint G, which is the midpoint of EF, are (-3, -3). The product of these coordinates is 9. None of the provided options match the correct answer.
Step-by-step explanation:
The question asks us to find the coordinates of the midpoint, G, of the line segment EF and then calculate the product of G's coordinates. To do this, we need to find the average of the x-coordinates and y-coordinates of points E (–19, –7) and F (13, 1) respectively.
The x-coordinate of G is the average of the x-coordinates of E and F: ((-19) + 13) / 2 = (-6) / 2 = -3.
The y-coordinate of G is the average of the y-coordinates of E and F: ((-7) + 1) / 2 = (-6) / 2 = -3.
Therefore, the coordinates of G are (-3, -3). To find the product of the coordinates, we multiply the x and y values: -3 * -3 = 9. However, none of the options provided (A: 48, B: 90, C: 104, D: 130) match the correct answer, which is 9.
To find the midpoint of two points, we can use the midpoint formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's substitute the given values:
M = ((-19 + 13) / 2, (-7 + 1) / 2)
M = (-6 / 2, -6 / 2)
M = (-3, -3)
The product of the x-coordinate and y-coordinate of the midpoint is (-3) * (-3) = 9