IDNLearn.com: Where questions are met with accurate and insightful answers. Get the information you need quickly and accurately with our reliable and thorough Q&A platform.
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].
[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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.