If the distance between $$ (x, x) $$ and $$ (7,7) $$ is 10 , where $$ x7 $$, then $$ x $$ is equal to

Question

If the distance between $$ (x, x) $$ and $$ (7,7) $$ is 10 , where $$ x>7 $$, then $$ x $$ is equal to

UpStudy AI · Accepted Answer

To find the value of $$ x $$ such that the distance between the points $$ (x, x) $$ and $$ (7, 7) $$ is 10, we can use the distance formula:

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

Applying the coordinates:

$$
10 = \sqrt{(x - 7)^2 + (x - 7)^2}
$$

Simplify the equation:

$$
10 = \sqrt{2(x - 7)^2}
$$

Square both sides to eliminate the square root:

$$
100 = 2(x - 7)^2
$$

Divide both sides by 2:

$$
50 = (x - 7)^2
$$

Take the square root of both sides:

$$
x - 7 = \sqrt{50} = 5\sqrt{2}
$$

Since $$ x > 7 $$, we add 7 to both sides:

$$
x = 7 + 5\sqrt{2}
$$

**Answer:** $$ x = 7 + 5\,\sqrt{2} $$
$$ x = 7 + 5\sqrt{2} $$

If the distance between \( (x, x) \) and \( (7,7) \) is 10 , where \( x>7 \), then \( x \) is equal to