Find point C on the xaxis so AC BC is a minimum A4 5 B12 3

Find point C on the x-axis so AC + BC is a minimum.

A(4, -5), B(12, 3)

Please show work.

Solution:

Points A(4, -5), B(12, 3) and C(x,0) must be collinear points so that AC + BC would be minimum

thus they must lie on the same line

Now we can find the equation of line using points A and B using point slope formula

(Y₂-Y₁)/ (X₂-X1) = (y-Y1)/(x-X1)

(3-(-5)) / (12-4) = (y-(-5))/(x-4)

8/8=( y+5)/(x-4)

x-4=y+5

y=x-9

for x intercept , plug y = 0

x = 9

therefore points C (9,0)

where AC +BC is minimum

Answer