Question

1. a line segment on the coordinate plane has endpoints (2,4) and (4,y). the midpoint of the segment is point (3,7). what is the value of y?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given endpoints \((2,4)\) and \((4,y)\) and mid - point \((3,7)\).
For the x - coordinate of the mid - point: \(\frac{2 + 4}{2}=3\) (which is correct as per the given mid - point x - coordinate).
For the y - coordinate of the mid - point: \(\frac{4 + y}{2}=7\).

Step2: Solve for y

Multiply both sides of the equation \(\frac{4 + y}{2}=7\) by 2: \(4 + y=14\).
Subtract 4 from both sides: \(y=14 - 4\).

Answer:

10