Question

Find the distance between the two points and the midpoint of the line segment joining the points. Please!!!

Answer 1

To find the distance between two points, use the distance formula. To find the midpoint of the line segment, use the midpoint formula.

Step-by-step explanation:

To find the distance between two points and the midpoint of the line segment joining them, you can use the distance formula and the midpoint formula.

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Midpoint formula: (xm, ym) = ((x1 + x2)/2, (y1 + y2)/2)

For example, if you have two points A(2, 3) and B(5, 7), the distance between them would be:

d = sqrt((5 - 2)^2 + (7 - 3)^2) = sqrt(9 + 16) = sqrt(25) = 5 units.

The midpoint of AB would be:

(xm, ym) = ((2 + 5)/2, (3 + 7)/2) = (3.5, 5)

Answer 2

The distance, d, between two points: (x1, y1) and (x2, y2) is computed as follows:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Substituting with the points (-2, 7) and (6,3), we get:

`\begin{gathered} d=\sqrt[]{(6-(-2))^2+(3-7)^2} \\ d=\sqrt[]{8^2+(-4)^2} \\ d=\sqrt[]{64+16} \\ d=\sqrt[]{80} \\ d\approx8.944 \end{gathered}`

The coordinates of the midpoint (xm, ym) are calculated as follows:

`(x_m,x_m)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Substituting with the points (-2, 7) and (6,3), we get:

`\begin{gathered} (x_m,x_m)=((-2+6)/(2),(7+3)/(2)) \\ (x_m,x_m)=(2,5) \end{gathered}`