A(1,-1), B(3,-4), C(6,-2), and D is an endpoint of rhombus. Determine distance B point to straight line from D and paralel with AC line?
+23254 Point D is (4, 1).
Slope of line AC: m = (-2 - -1)/(6 - 1) = -1/5
Line through D parallel to AC: y - 1 = (-1/5)(x - 4) ---> x + 5y = 9
Distance from point B to that line must have a slope perpendicular to that line and pass through (3, -4):
y + 4 = 5(x - 3) ---> 5x - y = 19
Find the point where the two lines intersect: x + 5y = 9 and 5x - y = 19 ---> (4, 1)
Find the distance from (3, -4) to (4, 1) ---> d = √[ (4 - 3)² + (1 - -4)² ] = √26
+23254 Point D is (4, 1).
Slope of line AC: m = (-2 - -1)/(6 - 1) = -1/5
Line through D parallel to AC: y - 1 = (-1/5)(x - 4) ---> x + 5y = 9
Distance from point B to that line must have a slope perpendicular to that line and pass through (3, -4):
y + 4 = 5(x - 3) ---> 5x - y = 19
Find the point where the two lines intersect: x + 5y = 9 and 5x - y = 19 ---> (4, 1)
Find the distance from (3, -4) to (4, 1) ---> d = √[ (4 - 3)² + (1 - -4)² ] = √26
