Question

J is located at (2,7) , q is located at (5,12) and m is located at ((x,y)

Answer 1

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Explanation:

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Answer 2

Since points J, Q, and M are collinear of JM, and JQ, the values of x and y as an ordered pair is (9.5, 19.5).

In this scenario, line ratio would be used to determine the coordinates of the point M on the directed line segment JM and JQ that partitions the segment into a ratio of 2 to 3.

In Mathematics and EuclideanGeometry, line ratio can be used to determine the coordinates of a point and this is modeled by this mathematical equation:

`M(x, y) = (((mx_2 + nx_1))/((m + n)), (((my_2 + ny_1))/((m + n)))`

By substituting the given points J (2, 7) and Q (5, 12) into the formula for line ratio, we have;

`M (x, y) = (((mx_2 + nx_1))/((m + n)), (((my_2 + ny_1))/((m + n)))\\\\ (5, 12) = ((( 2(x) + 3(2))/((2 + 3)), (((3(7) + 2(y)))/((2 + 3)))`

By solving the equation in part for the value of x and y, we have;

`5 =(( 2x + 6))/(5)\\\\25=2x+6\\\\`

2x = 25 - 6

x = 19/2

x = 9.5

`12 = ((21 + 2y))/((5))\\\\60 = 21 + 2y`

2y = 60 - 21

y = 39/2

y = 19.5

In conclusion, we can logically deduce that point M is located at (9.5, 19.5).

Complete Question:

Points J,Q, and M are collinear of JM, and JQ: QM=2/3.

J is located at (2,7), Q is located at (5,12), and M is located at (x, y).

What are the values of x and y?