Final answer:
The coordinates of point P that partitions the line segment AB in a 1 to 4 ratio, given A(-1, 1) and B(7, 3), are (0.6, 1.4). The formula for the internal division of a segment in a given ratio was used to find these coordinates.
Step-by-step explanation:
The student's question is asking to find the coordinates of point P that divides the line segment AB in a 1 to 4 ratio given the coordinates A(-1, 1) and B(7, 3). To solve this, we use the formula for internal division of a segment in a ratio, which can be stated as:
Mx = (x1b + x2a) / (a + b)
My = (y1b + y2a) / (a + b) where
(x1, y1) are the coordinates of point A
(x2, y2) are the coordinates of point B
a and b represent the ratio which point P divides AB
(Mx, My) are the coordinates of point P
Substituting the given coordinates and ratio, we find:
Mx = ((-1) * 4 + 7 * 1) / (1 + 4) = 3 / 5 = 0.6
My = (1 * 4 + 3 * 1) / (1 + 4) = 7 / 5 = 1.4
Therefore, the coordinates of point P are (0.6, 1.4).