Find the distance between the two points. $$ (1,-3) $$ and $$ (61,22) $$

Question

UpStudy AI · Accepted Answer

1. First, recall the distance formula between two points $$ (x_1,y_1) $$ and $$ (x_2,y_2) $$:
   $$
   d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
   $$

2. For the points $$ (1,-3) $$ and $$ (61,22) $$, assign:
   $$
   x_1 = 1,\quad y_1 = -3,\quad x_2 = 61,\quad y_2 = 22
   $$

3. Substitute these values into the distance formula:
   $$
   d = \sqrt{(61-1)^2+(22-(-3))^2}
   $$
   $$
   d = \sqrt{(60)^2+(25)^2}
   $$

4. Calculate the squares:
   $$
   (60)^2 = 3600,\quad (25)^2 = 625
   $$
   Thus:
   $$
   d = \sqrt{3600+625}
   $$

5. Add the values inside the square root:
   $$
   d = \sqrt{4225}
   $$

6. Finally, compute the square root:
   $$
   d = 65
   $$

The distance between the two points is $$ 65 $$.
The distance between the points $$ (1,-3) $$ and $$ (61,22) $$ is 65.

Find the distance
between the two points.
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