exercise

[veiko]

In the coordinate plane (Oxy ), for the point (M( (4;( rm( 1)))) ), the line (d ) through (M ), (d ) intersects the ray (Ox ), (Oy ) times turns at (A( (a;( rm( 0)))) ), (B( (0;( rm( ))b) ) ) such that the triangle (ABO ) ( (O ) is the origin) has smallest area. The value (a - 4b ) is equal to

A:-14
B: 0
C:8
D:-2

Help me?

[janusz55]

Please rewrite the exercice using the \( \LaTeX \) editor, because this content is unreadable.

[wornmouth]

This appears to be a math word problem involving coordinates and geometry. Based on the details provided:

- There is a point M(4, 1)
- A line d goes through point M
- Line d intersects the x and y axes at points A(a, 0) and B(0, b) respectively
- We want to find a and b such that triangle ABO has the smallest possible area

To minimize the area of triangle ABO:
- Make the base AB as small as possible
- The lowest value of AB is when A and B are both on the y-axis
- This would make a = 0
-Plugging a = 0 into the given equation a - 4b = ?
- We get: 0 - 4b = ?
-Therefore, the value of a - 4b is 0

The answer is B

I walked through the logic and mathematical reasoning to determine why the value a - 4b must be 0 given the constraints provided in the problem.