Question

JK is on the coordinate plane with J located at (7, -5) and Klocated at(-5,3). L is a point on JK that is 3 times closer to point than it is topoint K. What are the coordinates of point L?A. (-2, 1)B. (1, -1)C. (2, -2)D. (4, -3)

Answer 1

The points J is given as,

$J=(x_{1,}y_1)=(7,-5)\text{ }$

The point K is given as,

$K=(x_{2,}y_2)=(-5,3)$

L is a point on JK that is 3 times closer to point J (assuming) than it is to point K.

Which means that the ratio is

$3\colon1$

The coordinates of point L can be found by,

$\frac{a\cdot x_1+b\cdot x_2}{a+b},\text{ }\frac{a\cdot y_1+b\cdot y_2}{a+b}$

Where a:b = 3:1

So let us substitute the given coordinates into the above equation

$\frac{3\cdot(7)+1\cdot(-5)}{3+1},\text{ }\frac{3\cdot(-5)+1\cdot(3)}{3+1}$

Simplify the equation,

$\frac{21-5}{4},\text{ }\frac{-15+3}{4}$$\frac{16}{4},\text{ }\frac{-12}{4}$$L=(4,-3)$

Therefore, the coordinates of point L are (4, -3)

The correct option is D.