Line segment AB¯¯¯¯¯¯¯¯ has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 16 of the way from A to B?
Responses
(823,−313)
(0,823)
(6,−313)
(2,6)
To find the coordinates of a point located a certain fraction of the way from point A to point B, we can use the following formula:
(x, y) = (x1 + t(x2 - x1), y1 + t(y2 - y1))
Where (x1, y1) are the coordinates of point A, (x2, y2) are the coordinates of point B, and t is the fraction of the way from A to B.
In this case, we want to find the coordinates of the point located 16 of the way from A to B. So, t = 16/100 = 0.16.
Plugging in the values, we get:
(x, y) = (1 + 0.16(7 - 1), 8 + 0.16(-4 - 8))
= (1 + 0.16 * 6, 8 + 0.16 * -12)
= (1 + 0.96, 8 - 1.92)
= (1.96, 6.08)
Therefore, the coordinates of the point located 16 of the way from A to B are (1.96, 6.08).
However, none of the provided answer choices match exactly with (1.96, 6.08), so none of the answer choices are correct.