Final answer:
To find the location of the point that is 3/4 of the distance from (-3,-10) to (5, 30), we calculate the total distance between the two points, which is sqrt(1664). Then, we find 3/4 of the distance by multiplying sqrt(1664) by 3/4. The point that is 3/4 of the distance is approximately (36.36, 0).
Step-by-step explanation:
To find the location of the point that is 3/4 of the distance from (-3,-10) to (5, 30), we need to calculate the total distance between the two points and then find the point that is 3/4 of that distance.
First, we calculate the distance between (-3,-10) and (5, 30) using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the values, we get d = sqrt((5 - (-3))^2 + (30 - (-10))^2) = sqrt(64 + 1600) = sqrt(1664).
Next, we find 3/4 of the distance by multiplying sqrt(1664) by 3/4. The result is 3/4 * sqrt(1664) = sqrt(1664) * 0.75 ≈ 36.36. So, the point that is 3/4 of the distance is approximately (36.36, 0). Therefore, the correct answer is A) (2, 0).