A. L1: (0,-1), (5,9) L2: (0,3), (4,1) The lines are perpendicular because there slopes product equal -1. The point they intersect is (1.6,2.2).(Is this true and how do you solve it)
To determine if the lines are perpendicular, we can check if the product of their slopes is equal to -1.
Let's start by finding the slopes of the lines. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:
slope = (y2 - y1) / (x2 - x1)
For Line 1 (L1), using the points (0, -1) and (5, 9), we can calculate the slope as follows:
slope_L1 = (9 - (-1)) / (5 - 0) = 10 / 5 = 2
For Line 2 (L2), using the points (0, 3) and (4, 1), we can calculate the slope as follows:
slope_L2 = (1 - 3) / (4 - 0) = -2 / 4 = -0.5
Now, let's check if the slopes are perpendicular by verifying if their product is equal to -1:
slope_L1 * slope_L2 = 2 * (-0.5) = -1
Since the product of the slopes is -1, we can conclude that the lines L1 and L2 are indeed perpendicular.
To find the point of intersection of the two lines, we can set their equations equal to each other and solve for the common values of x and y. Let's use the point-slope form for this:
For L1: y - y1 = m1(x - x1)
y - (-1) = 2(x - 0)
y + 1 = 2x
For L2: y - y2 = m2(x - x2)
y - 1 = -0.5(x - 4)
y - 1 = -0.5x + 2
Now, we can set these two equations equal to each other:
2x + 1 = -0.5x + 2
Simplifying this equation, we get:
2x + 0.5x = 2 - 1
2.5x = 1
x = 1 / 2.5
x = 0.4
Now, substitute the value of x back into either equation to find the value of y. Let's use the equation for L1:
y + 1 = 2(0.4)
y + 1 = 0.8
y = 0.8 - 1
y = -0.2
Therefore, the point of intersection is (0.4, -0.2). The given point (1.6, 2.2) does not coincide with the calculated point of intersection.