Question

what is the area of triangle lmn? 3 square units 4 square units 6 square units 8 square units

Explanation:

Step1: Find the base and height

Let's consider \( LN \) as the base. The length of \( LN \) is \( 3 - (- 1)=4 \) units (using the \( y - \)coordinates of \( N(1,3) \) and \( L(1,-1) \)). The horizontal distance from \( M(3,2) \) to the line \( x = 1 \) (the line containing \( LN \)) is the height. The height \( h=3 - 1 = 2 \) units.

Step2: Use the area formula for a triangle

The area formula for a triangle is \( A=\frac{1}{2}\times base\times height \). Substitute \( base = 4 \) and \( height=2 \) into the formula: \( A=\frac{1}{2}\times4\times2 \).

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Answer:

4 square units