+302 The points (1, 7), (13, 16) and (7,k), where k is an integer, are vertices of a triangle. What is the sum of the values of kfor which the area of the triangle is a minimum?
+302 CPhill, after answering this question, are you able to check on the last problem, becuase I don't think your answer is correct. Thank you!
+129852 Slope between the frist two points
[16-7]/[13-1]= 9/12 = 3/4
Equation of line through these two points
y = (3/4) (x -1) + 7 put into standard form
4y = 3(x -1) + 28
4y = 3x - 3 + 28
3x - 4y + 25 = 0
Using the partial formula for the distance between a point and a line, we want to minimize this
l 3(7) - 4(k) + 25 l = 0
l-4k + 46 l = 0
-4k = -46
k = 46/4 = 11.5
The integer values above and below this that are closest to 11.5 are k = 11 and k =12
Their sum = 23
Here's a graph
