Question

Point E is located at (2, −3), and point F is located at (−2, −1). Find the y-value for the point that is 3 over 4 the distance from point E to point F. −2. 5 −2 −1 −1. 5.

Answer 1

The ratio of the two point is the coordinate at the plane where the two point are divided at the fixed amount of length. The y value of the point that is 3/4 distance from point E to point F is -1.5. thus the option 4 is the correct option.

Given information-

The coordinates of the point E is (2,-3).

the coordinates of the point F is (-2,-1).

As the 3/4 the distance from the point E is the point F is means the points which divides the line EF in the ratio of 3/1.

Ratio of two point

The ratio of the two point is the coordinate at the plane where the two point are divided at the fixed amount of length.

Suppose the ratio $m:l$ are the ratio of the two points $(x_1,y_1)$ and $(x_2,y_2)$. Then the coordinate of the point which divide the line at this ratio can be given as,

$(x,y)=\left ( \dfrac{mx_2+lx_1\tiems}{m+l} ,\dfrac{my_2+ly_1}{m+l} \right )$

Put the values,

$(x,y)=\left ( \dfrac{3\times (-2)+1\times(2)}{3+1} ,\dfrac{3\times (-1)+1\times(-3)}{3+1} \right )$

$(x,y)=(-1,-1.5)$

Thus the y value of the point that is 3/4 distance from point E to point F is -1.5. thus the option 4 is the correct option.

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