The line joining the points (8,2),(−5,3) is neither parallel nor perpendicular to the line passing through points (16,6) and (3,15).
True
We know that, slope(m) of the line formed by joining the points (x1,y1) and (x2,y2) is given by
m=y2−y1x2−x1
Consider points A(8,2) and B(−5,3).
Then, slope of AB=3−2−5−8=−113=m1 (say)
Now, consider points P(16,6) and Q(3,15).
Then, slope of PQ=15−63−16=−913=m2 (say)
We see that m1≠m2 and hence AB and PQ are not parallel.
Also, m1×m2≠−1 and hence AB and PQ are not perpendicular to each other.
Therefore, the given statement is true.