The coordinates of point T are: (-1,4)
Step-by-step explanation:
The coordinates of a point that divides a line in m:n are given by the formula
[tex]T(x,y) = (\frac{nx_1+mx_2}{m+n}, \frac{ny_1+my_2}{m+n})[/tex]
Given
R(-5,12) = (x1,y1)
S(4,-6) = (x2,y2)
m = 4
n = 5
Putting the values
[tex]T(x,y) = (\frac{(5)(-5)+(4)(4)}{4+5}, \frac{(5)(12)+(4)(-6)}{4+5})\\T(x,y) = (\frac{-25+16}{9}, \frac{60-24}{9})\\T(x,y) = (\frac{-9}{9}, \frac{36}{9})\\T(x,y) = (-1,4)[/tex]
So,
The coordinates of point T are: (-1,4)
Keywords: Coordinate geometry, points
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