GEOMETRY The midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. The length of the midsegment is related to the length of the third side of the triangle. If the third side of the triangle is 2 inches then the length of the midsegment is 1 inch. If the third side of the triangle is 6 inches, then the length of the midsegment is 3 inches. Write an equation in point-slope form to find the length y,in inches, of the midsegment of a triangle whose third side has a length of x inches.

## Step 1<br />The problem provides two sets of data: (2,1) and (6,3). These represent the length of the third side (x) and the length of the midsegment (y) of the triangle. <br /><br />## Step 2<br />We can use these data points to find the slope of the line that represents the relationship between x and y. The slope (m) is calculated using the formula:<br />### \(m = \frac{y2 - y1}{x2 - x1}\)<br /><br />## Step 3<br />Substituting the given data points into the formula, we get:<br />### \(m = \frac{3 - 1}{6 - 2} = \frac{2}{4} = 0.5\)<br /><br />## Step 4<br />The point-slope form of a linear equation is given by:<br />### \(y - y1 = m(x - x1)\)<br /><br />## Step 5<br />We can use one of the given data points (2,1) and the slope we found (0.5) to write the equation of the line. Substituting these values into the point-slope form, we get:<br />### \(y - 1 = 0.5(x - 2)\)