Question

what is the area of triangle rst? 6 square units 9 square units 12 square units 18 square units

Explanation:

Step1: Find the base of the triangle

The base \(RS\) can be found by counting the units on the grid. \(R\) is at \(x=-2\) and \(S\) is at \(x = 3\). The length of \(RS\) is \(3-(-2)=5\) units. Wait, no, another way: Using the formula for the distance between two points on a horizontal line (since \(y - coordinate\) of \(R\) and \(S\) is \(2\)). The distance \(d=\vert x_2 - x_1\vert\). If \(R(-2,2)\) and \(S(3,2)\), then \(RS=\vert3-(-2)\vert = 5\) units. Wait, no, better use the formula for the area of a triangle \(A=\frac{1}{2}\times base\times height\). The vertical distance (height) from \(T(-1,- 1)\) to the line \(y = 2\) (where \(R\) and \(S\) lie) is \(h=\vert2-(-1)\vert=3\) units. The base \(RS\): since \(R(-2,2)\) and \(S(3,2)\), \(RS=\vert3 - (-2)\vert=5\) units? No, wait, no! Wait, the formula \(A=\frac{1}{2}\times base\times height\). The base \(RS\): count the number of units between \(R\) and \(S\) on the same horizontal line (\(y = 2\)). From \(x=-2\) to \(x = 3\), that's \(3-(-2)=6\) units (counting the grids: from \(-2\) to \(3\) is \(6\) units). The height is the vertical distance from \(T\) to the line \(RS\). \(R\) and \(S\) have \(y = 2\), \(T\) has \(y=-1\). The height \(h=\vert2-(-1)\vert = 3\) units.

Step2: Calculate the area

Using the formula \(A=\frac{1}{2}\times base\times height\). Substitute \(base = 6\) and \(height=3\). Then \(A=\frac{1}{2}\times6\times3\).

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Answer:

9 square units