Question

does adding 7+2 and then dividing by 2 help you find the find midpoint of line segment (overline{jk})?
(1 point)
no because (7,2) is not the coordinate of point j or k.
yes because (7+2)+2 calculates the average, or midpoint, of the y - coordinates of points j and k
yes because (7+2)+2 calculates the average, or midpoint, of the x - coordinates of points j and k
no because 7 should be added to 3, then multiplied by 2 to find the midpoint.

Explanation:

To find the midpoint of a line segment, we use the midpoint formula, which involves averaging the x - coordinates and the y - coordinates of the two endpoints. First, we need to determine the coordinates of points \(J\) and \(K\). From the graph, we can see that point \(J\) has coordinates \((- 6,7)\) and point \(K\) has coordinates \((4,2)\).

The formula for the midpoint \(M=(x_m,y_m)\) of a line segment with endpoints \((x_1,y_1)\) and \((x_2,y_2)\) is \(x_m=\frac{x_1 + x_2}{2}\) and \(y_m=\frac{y_1 + y_2}{2}\).

For the y - coordinates of \(J\) and \(K\), \(y_1 = 7\) and \(y_2=2\). The average of the y - coordinates is \(\frac{7 + 2}{2}\), which is exactly the operation of adding 7 and 2 and then dividing by 2. This operation is used to find the midpoint of the y - coordinates of the two points.

Now let's analyze the options:

• Option 1: \((7,2)\) is not a coordinate of \(J\) or \(K\), but this is not relevant to whether \(\frac{7 + 2}{2}\) helps find the midpoint. The midpoint formula uses the average of coordinates, not checking if the numbers are coordinates of the points. So this option is incorrect.
• Option 2: As we saw, \(\frac{7+2}{2}\) calculates the average of the y - coordinates of \(J\) and \(K\), which is part of finding the midpoint (the y - coordinate of the midpoint). So this option is correct.
• Option 3: The x - coordinates of \(J\) and \(K\) are \(-6\) and \(4\), not 7 and 2. So \(\frac{7 + 2}{2}\) does not calculate the average of the x - coordinates. This option is incorrect.
• Option 4: The midpoint formula is about averaging coordinates, not adding 7 to 3 and multiplying by 2. This option is incorrect.

Answer:

Yes because \((7 + 2)\div2\) calculates the average, or midpoint, of the y - coordinates of points \(J\) and \(K\)