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Answer:
P(1, -5)
Step-by-step explanation:
The segment must be divided into two parts in the ratio of 3:4.
That means the segment length to one part to the other part are in the ratio 7:3:4.
We find the distance in x and in y between the points, and we divide the horizontal and vertical distances in the same ratio.
Horizontal distance:
From x = 7 to x = -7, the distance is 14.
We need to divide a distance of 14 into two segments with the ratio of 3:4.
7x:3x:4x
14:3x:4x
14 = 3x + 4x
14 = 7x
The change in x = 2
7x:3x:4x
14:6:8
The distance in x from A is 6.
7 - 6 = 1
The x-coordinate is 1
Vertical distance:
From x = -8 to x = -1, the distance is 7.
We can easily conclude that to divide 7 into two parts with a ratio of 3:4, the parts will measure 3 and 4.
The change in y = 3
The distance in y from A is 3.
-8 + 3 = -5
The y-coordinate is -5
Answer: P(1, -5)