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
`(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((2* (-2)+1* 3)/(2+1),(2* 3+1* (-1))/(2+1)\right)\\\\\\=\left((-4+3)/(3),(6-1)/(3)\right)\\\\=\left((-1)/(3),(5)/(3)\right).`

Thus, the y-value of the point P is
`(5)/(3).`