Answer:
To find the value of x such that JK is perpendicular to LM, we can use the concept of slope.
The slope of JK can be found using the formula:
slope(JK) = (y2 - y1) / (x2 - x1)
Substituting the given coordinates for J(8, -3) and K(7, -1) into the formula:
slope(JK) = (-1 - (-3)) / (7 - 8) = 2 / -1 = -2
To determine whether JK is perpendicular to LM, we need to find the slope of LM.
The slope of LM can be found using the formula:
slope(LM) = (y2 - y1) / (x2 - x1)
Substituting the given coordinates for L(1, -1) and M(x, 2) into the formula:
slope(LM) = (2 - (-1)) / (x - 1) = 3 / (x - 1)
Since JK is perpendicular to LM, the product of their slopes should be -1. Therefore:
(-2) * (3 / (x - 1)) = -1
Simplifying the equation:
-6 / (x - 1) = -1
To solve for x, we can cross multiply:
-6 = -(x - 1)
Distributing the negative sign:
-6 = -x + 1
Adding x to both sides:
-x - 6 = 1
Adding 6 to both sides:
-x = 7
Multiplying both sides by -1:
x = 7
Therefore, when x = 7, JK is perpendicular to LM.