If a road passes through R(4,-11) and S (0, -9) and another road passes through J (6,-2) and K(4, -5) and are straight lines, are the two roads perpendicular and why?

To determine if the two roads are perpendicular, we need to check if the slopes of the two lines are negative reciprocals of each other.

Let's calculate the slope of the first road passing through R(4,-11) and S(0, -9):

Slope of RS = (change in y-coordinates) / (change in x-coordinates)
= (-9 - (-11)) / (0 - 4)
= (-9 + 11) / (-4)
= 2 / (-4)
= -1/2

Similarly, let's calculate the slope of the second road passing through J(6,-2) and K(4, -5):

Slope of JK = (change in y-coordinates) / (change in x-coordinates)
= (-5 - (-2)) / (4 - 6)
= (-5 + 2) / (4 - 6)
= -3 / (-2)
= 3/2

The slopes of the two roads are -1/2 and 3/2, respectively.

To determine if the two roads are perpendicular, we need to check if the product of their slopes is -1.

(-1/2) * (3/2) = -3/4 ≠ -1

Since the product of the slopes is not -1, the two roads are not perpendicular to each other.