Respuesta :
Answer:
the point C(x,0) = C(3,0) is the point where AC + BC is minimum.
Step-by-step explanation:
Solution:
This question is very simple to solve.
We need to find the x and y elements of point C, which is on the x-axis such that AC + BC = minimum.
So,
As, we have said that, point C is on the x-axis then, it means its y co ordinate will be equals to zero.
Now, we just need to find x co ordinate of the point C.
C (x, 0) as it is on the y -axis.
So, for that, we need to take the mirror image of point B. It means, its x co-ordinate will remain same but y co-ordinate will be negative.
So, our mirror image of B(6,9) = B'(6,-9)
Now, we have to join the points A and B'. Point C, which we are trying to find is the point where this line AB' intersects with x - axis.
So,
Slope of the line AB'
m = [tex]\frac{y1-y2}{x1-x2}[/tex]
m = [tex]\frac{3- - 9}{2 - 6}[/tex] = [tex]\frac{3+9}{2-6}[/tex]
m = [tex]\frac{12}{-4}[/tex] = -3
m = slope = -3
We also know that the equation of line:
y = mx + b
where b = y-intercept.
Now, we need to find the y - intercept of this line.
y = (-3) x + b
where y = -9 and x = 6
so,
-9 = (-3) (6) + b
b = -9 + 18
b = 9 = y - intercept.
SO,
y = mx + b
and For point C(x, 0) y = 0
0 = -3x + 9
Solve for x:
3x = 9
x = 3
Hence, the point C(x,0) = C(3,0) is the point where AC + BC is minimum.
