Question 5: If the distance between $$ (2, y) $$ and $$ (8,6) $$ is 10 , where $$ y \geqslant 0 $$, then $$ y $$ is equat to

Question

UpStudy AI · Accepted Answer

To find the value of $$ y $$ such that the distance between the points $$ (2, y) $$ and $$ (8, 6) $$ is 10, we'll use the distance formula:

$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Plugging in the given points and distance:

$$
10 = \sqrt{(8 - 2)^2 + (6 - y)^2}
$$

Simplify the equation:

$$
10 = \sqrt{6^2 + (6 - y)^2}
$$
$$
10 = \sqrt{36 + (6 - y)^2}
$$

Square both sides to eliminate the square root:

$$
100 = 36 + (6 - y)^2
$$
$$
(6 - y)^2 = 64
$$

Take the square root of both sides:

$$
6 - y = \pm 8
$$

This gives us two possible solutions:

1. $$ 6 - y = 8 $$  
   $$ y = 6 - 8 = -2 $$  
   However, since $$ y \geq 0 $$, this solution is discarded.

2. $$ 6 - y = -8 $$  
   $$ y = 6 + 8 = 14 $$

**Therefore, the value of $$ y $$ is 14.**

Answer: 14
$$ y = 14 $$

Question 5: If the distance between \( (2, y) \) and \( (8,6) \) is 10 , where \( y \geqslant 0 \), then \( y \) is equat to