Question

Point G is located at (3, −1) and point H is located at (−2, 3). Find y value for the point that is 2 over 3 the distance from point G to point H.

Answer 1

B. 1.67
m : n = 2 : 1
 ( x, y ) = ( (1*3 + 2*(-2))/(2+1) ;  (1 * (-1) + 2 * 3) /(2 + 1) ) =
 = ( (3-4)/3  ; (-1+6)/3 ) 1.67

Answer 2

Answer: The answer is $\dfrac{5}{3}.$

Step-by-step explanation:  Given that the co-ordinates of point G and H are (3, -1) and (-2, 3) respectively.

We are to find the y-value of the point P that is located at two-third distance from point G to point H.

As shown in the attached figure, the ration in which the point P divides the line segment GH is 2 : 1.

Therefore, the co-ordinates of point P will be

$\left(\dfrac{2\times (-2)+1\times 3}{2+1},\dfrac{2\times 3+1\times (-1)}{2+1}\right)\\\\\\=\left(\dfrac{-4+3}{3},\dfrac{6-1}{3}\right)\\\\=\left(\dfrac{-1}{3},\dfrac{5}{3}\right).$

Thus, the y-value of the point P is $\dfrac{5}{3}.$