Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

19. Elein and Naya wanted to meet between their
houses at midpoint (4,1). If Elien's house is at point
A. (7,-1.5)
(10,-4).
B. (-2,6)
Find the coordinates of Naya's house.
C. (0,0)

Sagot :

MrRoyal

Answer:

[tex](-2,6)[/tex]

Step-by-step explanation:

Given

[tex]Elena = (10,-4)[/tex]

[tex]Midpoint = (4,1)[/tex]

Required

Determine the coordinates of Naya's

Midpoint is calculated as:

[tex]M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]

In this case:

[tex](x_1,y_1) = (10,-4)[/tex]

[tex](x,y) = (4,1)[/tex]

So, we have:

[tex](4,1) = \frac{1}{2}(10+x_2,-4+y_2)[/tex]

Multiply through by 2

[tex]2 * (4,1) = \frac{1}{2}(10+x_2,-4+y_2) * 2[/tex]

[tex](8,2) = (10+x_2,-4+y_2)[/tex]

By comparison:

[tex]8 = 10 + x_2[/tex]

[tex]2 = -4 + y_2[/tex]

So:

[tex]8 = 10 + x_2[/tex]

[tex]x_2 = 8 - 10[/tex]

[tex]x_2 = -2[/tex]

[tex]2 = -4 + y_2[/tex]

[tex]y_2 =2+4[/tex]

[tex]y_2 =6[/tex]

So, the coordinate is: [tex](-2,6)[/tex]

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.