Get the information you need from a community of experts on IDNLearn.com. Our Q&A platform offers reliable and thorough answers to ensure you have the information you need to succeed in any situation.

What is the other endpoint if one endpoint is (10,12) and the midpoint is (6,9).?

Sagot :

Answer:

[tex](2,\, 6)[/tex].

Step-by-step explanation:

Let [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] denote the two endpoints.

The formula for the midpoint of these two points would be:

[tex]\displaystyle \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)[/tex].

(Similar to taking the average of each coordinate.)

In this question, it is given that [tex]x_{0} = 10[/tex] whereas [tex]y_{0} = 12[/tex]. Substitute these two values into the expression for the coordinate of the midpoint:

  • [tex]x[/tex]-coordinate of the midpoint: [tex]\displaystyle \frac{10 + x_{1}}{2} = 6[/tex].
  • [tex]y[/tex]-coordinate of the midpoint: [tex]\displaystyle \frac{12 + y_{1}}{2} = 9[/tex].

Solve these two equations for [tex]x_{1}[/tex] and [tex]y_{1}[/tex]: [tex]x_{1} = 2[/tex] whereas [tex]y_{1} = 6[/tex].

Hence, the coordinate of the other point would be [tex](2,\, 6)[/tex].

We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.