Question

1. practice: using visual cues fill in the blanks to explain the midpoint formula. midpoint formula midpoint = (\\(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2}\\)) (x_1,y_1) = first (x_2,y_2) = second \\(\frac{x_1 + x_2}{2}=\\) _ of x - coordinates \\(\frac{y_1 + y_2}{2}=\\) _ of y - coordinates

Explanation:

Step1: Recall mid - point formula concept

The mid - point of a line segment with endpoints \((x_1,y_1)\) and \((x_2,y_2)\) has its \(x\) - coordinate as the average of the \(x\) - coordinates of the endpoints and its \(y\) - coordinate as the average of the \(y\) - coordinates of the endpoints.

Step2: Identify parts of the formula

The mid - point formula for the \(x\) - coordinate of the mid - point of a line segment with endpoints \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{x_1 + x_2}{2}\), where \(x_1\) is the \(x\) - coordinate of the first point \((x_1,y_1)\) and \(x_2\) is the \(x\) - coordinate of the second point \((x_2,y_2)\). Similarly, for the \(y\) - coordinate, it is \(\frac{y_1 + y_2}{2}\), where \(y_1\) is the \(y\) - coordinate of the first point \((x_1,y_1)\) and \(y_2\) is the \(y\) - coordinate of the second point \((x_2,y_2)\).

Answer:

midpoint \(=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\) where \((x_1,y_1)\) is the first point and \((x_2,y_2)\) is the second point. The \(x\) - coordinate of the mid - point is \(\frac{x_1 + x_2}{2}\) (average of \(x\) - coordinates of endpoints) and the \(y\) - coordinate of the mid - point is \(\frac{y_1 + y_2}{2}\) (average of \(y\) - coordinates of endpoints).