IDNLearn.com: Your trusted source for finding accurate answers. Get the information you need from our community of experts, who provide detailed and trustworthy answers.
Sagot :
To find the midpoint of the line segment with endpoints [tex]\( G (10, 1) \)[/tex] and [tex]\( H (3, 5) \)[/tex], we use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Starting with the coordinates of point [tex]\( G \)[/tex], which are [tex]\( (10, 1) \)[/tex], and the coordinates of point [tex]\( H \)[/tex], which are [tex]\( (3, 5) \)[/tex]:
1. Calculate the [tex]\( x \)[/tex]-coordinate of the midpoint.
[tex]\[ \text{Midpoint}_x = \frac{10 + 3}{2} = \frac{13}{2} = 6.5 \][/tex]
2. Calculate the [tex]\( y \)[/tex]-coordinate of the midpoint.
[tex]\[ \text{Midpoint}_y = \frac{1 + 5}{2} = \frac{6}{2} = 3 \][/tex]
Thus, the coordinates of the midpoint are:
[tex]\[ (6.5, 3.0) \][/tex]
Therefore, the closest answer in the given options is:
C. [tex]\(\left(\frac{13}{2}, 3\right)\)[/tex]
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Starting with the coordinates of point [tex]\( G \)[/tex], which are [tex]\( (10, 1) \)[/tex], and the coordinates of point [tex]\( H \)[/tex], which are [tex]\( (3, 5) \)[/tex]:
1. Calculate the [tex]\( x \)[/tex]-coordinate of the midpoint.
[tex]\[ \text{Midpoint}_x = \frac{10 + 3}{2} = \frac{13}{2} = 6.5 \][/tex]
2. Calculate the [tex]\( y \)[/tex]-coordinate of the midpoint.
[tex]\[ \text{Midpoint}_y = \frac{1 + 5}{2} = \frac{6}{2} = 3 \][/tex]
Thus, the coordinates of the midpoint are:
[tex]\[ (6.5, 3.0) \][/tex]
Therefore, the closest answer in the given options is:
C. [tex]\(\left(\frac{13}{2}, 3\right)\)[/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.