Alice and her friend want to meet for lunch at a point halfway between their homes. Alice's home can be represented by the point left parenthesis negative 1 comma 2 right parenthesis and her friend's home by the point left parenthesis 3 comma 4 right parenthesis. What are the coordinates of the point that represents the location where they should meet?

Question

(1 point)
Responses

left parenthesis 2 comma 1 right parenthesis
Image with alt text: left parenthesis 2 comma 1 right parenthesis

left parenthesis one half comma Start Fraction 7 over 2 End Fraction right parenthesis
Image with alt text: left parenthesis one half comma Start Fraction 7 over 2 End Fraction right parenthesis

left parenthesis Start Fraction 3 over 2 End Fraction comma Start Fraction 5 over 2 End Fraction right parenthesis
Image with alt text: left parenthesis Start Fraction 3 over 2 End Fraction comma Start Fraction 5 over 2 End Fraction right parenthesis

left parenthesis 1 comma 3 right parenthesis

Answer 1

To find the point that represents the location where Alice and her friend should meet, we need to calculate the midpoint between their two homes. The coordinates of Alice's home are \((-1, 2)\) and her friend's home is \((3, 4)\).

The formula for the midpoint \((x_m, y_m)\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ (x_m, y_m) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Substituting the coordinates of Alice and her friend's homes into the formula:

\[ x_m = \frac{-1 + 3}{2} = \frac{2}{2} = 1 \]

\[ y_m = \frac{2 + 4}{2} = \frac{6}{2} = 3 \]

Thus, the midpoint, which represents the location where they should meet, is \((1, 3)\).

Therefore, the correct answer is:

\(\left( 1, 3 \right)\)