The value of x is D) -0.6.
The coordinates of A are (-3,5) and the coordinates of B are (3,0).
Point C cuts the line segment AB in the ratio of 2:3.
If any point C cut the line segment AB with vertices A(a,b) and B(c,d) in the ratio m:n, then the coordinates of point C(e,f) are given by:
c = m c + n a / m + n and f = m d + n b / m+ n
Here we have m = 2 and n = 3
a = - 3 ,b = 5 and c = 3 and d = 0.
Hence,
c = 2 * 3 + 3 * ( - 3 ) / 2 + 3
= - 3 / 5
= - 0 . 6
and
f = 2 * 0 + 3 * 5 / 2 + 3
= 15 / 5
= 3
Hence the coordinates of point C is (-0.6,3).
Hence, the x-value of point C is -0.6.
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