Question

Which coordinate K on the line segment with endpoints J (4,2) and L (4,6) divides JL such that the ratio of JK:KL is 3:1? helpp for finals!!
A. (4,5)
B. (5,4)
C. (4,3)
D. (3,4)

Answer 1

The answer for this question is letter D . ( 3,4) !!!!

Answer 2

The coordinate of K on the line segment JL is (4,5).

What is section formula?

When a point divides a line segment externally or internally in some ratio, we use section formula to find the coordinates of that point.

Internal section formula

$P(x, y) = (\frac{mx_{2} +nx_{1} }{m+n} ,\frac{my_{2}+ny_{1} }{m+n})$

Where,

(x, y) are the coordinates of point P.

$(x_{1},y_{1} )$ are the coordinates of point A.

$(x_{2},y_{2})$ are the coordinates of point B.

m and n are the ratio values in which P divides the line segment AB internally.

According to the given question.

Coordinates of points J and L are (4, 2) and (4, 6) respectively.

K divides the line segment JL in the ration 3:1.

Therefore, the coordinates of K by section formula is given by

$K(x, y) = (\frac{3(4)+1(4)}{3+1} , \frac{3(6)+1(2)}{3+1} )$

⇒ $K(x, y) = (\frac{12+4}{4} , \frac{18 + 2}{4} )$

⇒ $K(x, y) = (\frac{16}{4} ,\frac{20}{4})$

⇒$K(x, y) = ( 4, 5)$

Hence, the coordinate of K on the line segment JL is (4,5).

Find out more information about section formula here:

https://brainly.com/question/20320420

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