Find the coordinates of p so that p partitions the segment ab in the ratio 1: 3 if a(5,8) and b(−1,4).
a. (3.5, 7)
b. (-6.5, -9)
c. (-4, -6)
d. (-1.5, -1)

Point of partition refers that a point intersect a particular line or curve at a fixed ratio. The coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).

The coordinates of the A is (5,8).

The coordinates of the B is (-1,4).

P partitions the segment AB in the ratio 1:3.

Point of partition refers that a point intersect a particular line or curve at a fixed ratio.

When a point intersect a line which has the coordinates and at a ratio l and m then this point can be represent as,

Put the values,

Hence the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).

Learn more about the point of partitions of a line here;

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The answer is A(3.5,7)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: