If $$ A $$ and $$ B $$ have the coordinates $$ (1,4) $$ and $$ (7,0) $$ respectively, find the exact length of $$ A B $$. (2 marks) submit Answer

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UpStudy AI · Accepted Answer

To find the exact length of segment $$ AB $$ with coordinates $$ A(1, 4) $$ and $$ B(7, 0) $$, we can use the **distance formula**:

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

**Step-by-Step Calculation:**

1. **Substitute the coordinates into the formula:**
   $$
   AB = \sqrt{(7 - 1)^2 + (0 - 4)^2}
   $$

2. **Calculate the differences:**
   $$
   AB = \sqrt{6^2 + (-4)^2}
   $$

3. **Square the differences:**
   $$
   AB = \sqrt{36 + 16}
   $$

4. **Sum the squares:**
   $$
   AB = \sqrt{52}
   $$

5. **Simplify the square root:**
   $$
   AB = 2\sqrt{13}
   $$

**Final Answer:**
The exact length of $$ AB $$ is $$ 2\sqrt{13} $$ units.
The exact length of $$ AB $$ is $$ 2\sqrt{13} $$ units.

If and have the coordinates and respectively, find
the exact length of .
(2 marks)
submit Answer