Final answer:
To find the x-coordinate of point P on the line segment AB that partitions it in a 7:7 ratio, we calculate the total distance of AB, determine the distance from A to P using the ratio, and find the x-coordinate of P by moving from A towards B by the AP distance.
Step-by-step explanation:
To find the x-coordinate of point P that partitions line segment AB in a 7:7 ratio, we first need to find the total distance of AB. The distance formula is used to calculate the distance between two points, which is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of A(-2, -10) and B(1, -5) into the formula gives us:
d = sqrt((1 - (-2))^2 + (-5 - (-10))^2) = sqrt(9 + 25) = sqrt(34)
Next, since AB is divided in a ratio of 7:7, we can determine the distance from A to P by multiplying the total distance by 7/14:
AP = (7/14) * sqrt(34)
To find the x-coordinate of P, we need to move from the x-coordinate of A towards the x-coordinate of B by a distance of AP. Since the ratio is equal, we divide the AP distance by the total distance along the x-axis and multiply by the difference in x-coordinates:
x-coordinate of P = -2 + ((7/14) * (1 - (-2)))
Calculating the expression gives us:
x-coordinate of P ≈ -2 + (7/14) * 3 = -1.5
Rounding this to the nearest whole number gives us -2 as the x-coordinate of P.