given the points P(6;5) ;Q (3;2) ; R(2m ;m+4) and T (5 /2 ;1 /2) calculate the value of m if PQ is parallel to RT
First, we need to calculate the slope of line PQ and line RT.
The slope of line PQ is given by:
m1 = (y2 - y1) / (x2 - x1)
m1 = (2 - 5) / (3 - 6)
m1 = -3 / -3
m1 = 1
The slope of line RT is given by:
m2 = (y2 - y1) / (x2 - x1)
m2 = (1/2 - 4) / (5/2 - 2m)
m2 = -7/2 / (5/2 - 2m)
m2 = -7/2 * 2 / 5 - 2m
m2 = -7 / 5 - 2m
Since line PQ is parallel to line RT, their slopes are equal.
Therefore, 1 = -7/5 - 2m
By solving for m, we get:
2m = -7/5 - 1
2m = -7/5 - 5/5
2m = -12/5
m = -6/5
Thus, the value of m is -6/5.