183k views
2 votes
Content loaded find the coordinates of point p that partitions line segment ab in a 1 to 4 ratio given a (-1, 1) and b (7, 3).

1 Answer

4 votes

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).

User Waleed Muaz
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories