IDNLearn.com offers a collaborative platform for sharing and gaining knowledge. Our platform offers comprehensive and accurate responses to help you make informed decisions on any topic.

Find the coordinates of the midpoint of the line segment joining the following pair of points.

a. [tex]\((5, 9)\)[/tex] and [tex]\((1, -1)\)[/tex]


Sagot :

To find the coordinates of the midpoint of a line segment joining two points, we can use the midpoint formula. The midpoint formula is given by:

[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.

Given points are:
[tex]\[ (5, 9) \quad \text{and} \quad (1, -1) \][/tex]

Let's apply the midpoint formula step by step:

1. Identify [tex]\(x_1\)[/tex], [tex]\(y_1\)[/tex], [tex]\(x_2\)[/tex], and [tex]\(y_2\)[/tex]:
[tex]\[ x_1 = 5, \quad y_1 = 9, \quad x_2 = 1, \quad y_2 = -1 \][/tex]

2. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{5 + 1}{2} = \frac{6}{2} = 3 \][/tex]

3. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{9 + (-1)}{2} = \frac{9 - 1}{2} = \frac{8}{2} = 4 \][/tex]

Therefore, the coordinates of the midpoint are:
[tex]\[ (3.0, 4.0) \][/tex]

Thus, the midpoint of the line segment joining the points [tex]\((5, 9)\)[/tex] and [tex]\((1, -1)\)[/tex] is [tex]\((3, 4)\)[/tex].