The coordinates of the endpoints of directed line segment ABC are A(- 8, 7) and C(7, - 13) . If AB / (BC) = 3/2 , the coordinates of B are
(-3,0)
(-2, -1)**
(1, -5)
(3, -6)
B is 3/5 of the way from A to C.
Going from A to C,
x changes by 15
y changes by -20
So, add 3/5 of those changes to A's coordinates to get to B.
To find the coordinates of point B, we can use the midpoint formula. The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
[(x1 + x2) / 2, (y1 + y2) / 2]
Using the coordinates of points A(-8, 7) and C(7, -13), we can calculate the coordinates of B:
x-coordinate of B: (-8 + 7) / 2 = -1 / 2 = -1/2
y-coordinate of B: (7 - 13) / 2 = -6 / 2 = -3
Therefore, the coordinates of point B are approximately (-1/2, -3). So the correct option is (-2, -1).
To find the coordinates of point B, we first need to calculate the length of AB and BC.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For AB:
x1 = -8
y1 = 7
x2 = ?
y2 = ?
Let's calculate the coordinates of B using the formula:
d = sqrt((-2 - (-8))^2 + (-1 - 7)^2)
= sqrt((6)^2 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100)
= 10
So, the length of AB is 10.
Similarly, for BC:
x1 = ?
y1 = ?
x2 = 7
y2 = -13
Using the distance formula:
d = sqrt((7 - (-2))^2 + (-13 - (-1))^2)
= sqrt((9)^2 + (-12)^2)
= sqrt(81 + 144)
= sqrt(225)
= 15
So, the length of BC is 15.
Now, we know that AB / BC = 3/2. We can set up the following equation:
10 / 15 = 3/2
Cross-multiplying:
2 * 10 = 3 * 15
20 = 45
Since 20 is not equal to 45, the given ratio is not correct.
Therefore, none of the options you provided for the coordinates of B are correct.