Question

Find the point L such that JL and KL form a 3:1 ratio.

Segment JK is shown. J is at (-3, 4). K is at (4,-2).

(−1.25, 2.5)

(−0.5, 1)

(2.25, −0.5)

(0.5, 2)

Answer 1

The correct option is 3.

Explanation:

The coordinates of end points of a line segment are (-3,4) and (4,-2).

Using section formula.

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

It is given that point L such that JL and KL form a 3:1 ratio.

`(x,y)=((3(4)+1(-3))/(3+1), (3(-2)+1(4))/(3+1))`

`(x,y)=((9)/(4), (-2)/(4))`

`(x,y)=(2.25, -0.5)`

Therefore the correct option is 3.

Answer 2

I graphed the points.

It forms an imaginary right triangle where JK serves as the hypotenuse. We simply use the Pythagorean theorem to solve for the measure of the segment.

long leg: -3 to 4 = 7 units
short leg: -2 to 4 = 6 units

c² = a² + b²
c² = 7² + 6²
c² = 49 + 36
c² = 85
c = √85
c = 9.22 or 9

9/4 = 2.25
2.25 * 3 = 6.75

Among the given choices, (2.25,-0.5) is the closest point of L to the segment JK