Answer:
Coordinates of the new library is (150, 70)
Step-by-step explanation:
To get the shortest possible distance means that line from point T to point R has to be perpendicular.
Now, the equation of R is given as;
y = x - 80 - - - (1)
For T to be perpendicular, it means it will have a slope equal to the negative reciprocal of line R.
Thus, slope of T is -1/1 = - 1
Thus, using line - slope intercept of y = mx + c, we can find equation of T as;
140 = -1(80) + c
140 = -80 + c
c = 140 + 80
c = 220
Thus, equation is;
y = -x + 220 - - - (eq 2)
Adding equation 1 to equation 2,we have;
y + y = 220 - 80
2y = 140
y = 140/2
y = 70
Putting 70 for y in eq 1 gives;
70 = x - 80
x = 70 + 80
x = 150
Thus;
Coordinate of the new library is (150, 70)
<---- Your answer....