Question

Find the point that splits segment GH in half if point G is located at (−3, 5) and point H is located at (0, −2).

(1, −1)
(4, 1)
(1.5, 3.5)
(−1.5, 1.5)

Answer 1

since it cuts it in half, ur looking for the midpoint
midpoint formula : (x1 + x2) / 2 , (y1 + y2)/2
(-3,5)...x1 = -3 and y1 = 5
(0,-2)..x2 = 0 and y2 = -2
now we sub and solve
m = (-3 + 0) / 2 , (5 - 2) / 2
m = (-3/2 , 3/2)
m = (-1.5, 1.5) <==

Answer 2

The point that splits segment GH in half if point G is located at (−3, 5) and point H is located at (0, −2) is:

(−1.5, 1.5)

Explanation:

Let C be the points that split the segment GH into two equal parts.

This means that C act as the mid-point of the line segment GH.

We know that the coordinate of the mid-point (e,f) of segment AB with vertices (a,b) and (c,d) respectively is given by:

`e=(a+c)/(2)\ ,\ f=(b+d)/(2)`

Here we have:

G(A,B)=G(-3,5) and H(c,d)=H(0,-2)

Hence, the vertices of C(e,f) are:

`e=(-3+0)/(2)\\\\\\e=-1.5`

and

`f=(5-2)/(2)\\\\\\f=1.5`

Hence, the coordinate of mid-point are:

(-1.5,1.5)