2
algebra

Find the area of the triangle formed by the line 2x+3y=122x + 3y = 12 and the coordinate axes.

A

1212

B

66

C

2424

D

44

Correct Answer: A

Choice A is the correct answer. Find intercepts.

  1. x-intercept: 2x=12x=62x = 12 \rightarrow x = 6. Base = 6.
  2. y-intercept: 3y=12y=43y = 12 \rightarrow y = 4. Height = 4.
  3. Area: 1/2×base×height=0.5×6×4=121/2 \times \text{base} \times \text{height} = 0.5 \times 6 \times 4 = 12.

💡 Strategic Tip: The axes form a right angle, so intercepts are base and height.

Choice B is incorrect because forgot 1/2? Choice C is incorrect because multiplied? Choice D is incorrect.