The first two points are
(7,3) and (8,7) --- line 1
(-5, -4) and (-1,-5)---- line 2
we can only determine whether a line is parallel, or perpendicular through slope
slope = y2 - y1/ x2 - x1
x1 = 7, y1 = 3 , x2 = 8, and y2 = 7
slope = 7 - 3 / 8 - 7
slope = 4 / 1
slope = 4
for the first line the slope is 4
second line
x1 = -5, y1 = -4, x2= -1, and y2 = -5
slope = -5 -(4) / -1 - (-5)
slope = -5 + 4/ -1 + 5
slope = -1 /4
slope = -1/4
slope is perpendicular when
m1 x m2 = -1
slope is parallel when
m1 = m2
for the first question the slope is perpendicular because
4 x -1/4 = -1
therefore line 1: (7,3) and (8,7) and line 2: (-5,-4) and (-1,-5) are perpendicular
question 2
(5,2) and (1,7) for the first line
(-1,3) and (9,-1) for the second line
slope = y2 - y1 / x2 - x1
slope = 7 - 2 / 1 - 5
slope = 5 / -4
for line 1 slope is -5/4
slope for line two
slope = y2 - y1/ x2 - x1
slope = -1 - 3/ 9 -(-1)
slope = -4 / 9 +1
slope = -4/10
slope = -2/5
since slope 1 and slope 2 are not the same, therefore the lines are not parallel
for perpendicular
-5/4 x -2/5 = 1/2
they are not perpendicual because the product of the two slopes is not equals to -1
last question
line one : (5,9) and (7,13)
line two: (0,2) and (4,10)
for line 1
slope = y2 - y1/ x2 - x1
slope = 13 - 9/ 7 - 5
slope = 4 / 2
slope = 2
for line 1 slope is 2
for line 2
slope = 10 - 2 / 4 - 0
slope= 8 /4
slope = 2
for line two slope is 2
therefore slope 1 and slope 2 are equal
slope 1 = slope 2
the lines are parallel to each other