can someone explain how to do this
Points A (-10,-6) and B (6,2) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 3/4 the length of AB?
a) (0,-1)
b) (2,0)
c) (-2,-2)
d) (4,1)
never mind i have the answer
To find the coordinates of point C on AB such that AC is 3/4 the length of AB, you can follow these steps:
1. Calculate the length of AB. The length of a line segment can be found using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of A are (-10, -6) and the coordinates of B are (6, 2). So, the length of AB is:
AB = sqrt((6 - (-10))^2 + (2 - (-6))^2)
2. Multiply the length of AB by 3/4 to find the length of AC:
AC = (3/4) * AB
3. Determine the coordinates of point C using the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) can be found by taking the average of the x-coordinates and the average of the y-coordinates:
x-coordinate of C = (x-coordinate of A + x-coordinate of B) / 2
y-coordinate of C = (y-coordinate of A + y-coordinate of B) / 2
4. Substitute the coordinates of A and B, along with the length of AC, into the midpoint formula to find the coordinates of C.
Let's apply these steps:
1. AB = sqrt((6 - (-10))^2 + (2 - (-6))^2)
AB = sqrt((16)^2 + (8)^2)
AB = sqrt(256 + 64)
AB = sqrt(320)
2. AC = (3/4) * AB
AC = (3/4) * sqrt(320)
AC = 3/4 * sqrt(320)
3. x-coordinate of C = (-10 + 6) / 2
x-coordinate of C = -4 / 2
x-coordinate of C = -2
y-coordinate of C = (-6 + 2) / 2
y-coordinate of C = -4 / 2
y-coordinate of C = -2
Therefore, the coordinates of point C on AB such that AC is 3/4 the length of AB are (-2, -2), which corresponds to option c).