Question

1. practice: using visual cues

fill in the blanks to explain the midpoint formula
midpoint formula
midpoint = (left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}
ight))
((x_1, y_1)) = first ______
((x_2, y_2)) = second ______
(\frac{x_1 + x_2}{2}) = ______ of x - coordinates

Explanation:

Step1: Analyze the first blank

In the midpoint formula context, \((x_1,y_1)\) represents the first point (or ordered pair) in a coordinate system, like a point on a line segment or in a plane. So the first blank should be "point (or ordered pair)".

Step2: Analyze the second blank

Similarly, \((x_2,y_2)\) is the second point (or ordered pair) for which we are finding the midpoint with the first point. So the second blank is "point (or ordered pair)".

Step3: Analyze the third blank

The formula \(\frac{x_1 + x_2}{2}\) is the average (or mean) of the \(x\)-coordinates of the two points \((x_1,y_1)\) and \((x_2,y_2)\), as it sums the two \(x\)-coordinates and divides by 2, which is the definition of the average. So the third blank is "average (or mean)".

Answer:

1. \((x_1,y_1)=\) first \(\boldsymbol{\text{point (or ordered pair)}}\)
2. \((x_2,y_2)=\) second \(\boldsymbol{\text{point (or ordered pair)}}\)
3. \(\frac{x_1 + x_2}{2}=\) \(\boldsymbol{\text{average (or mean)}}\) of \(x\)-coordinates