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

Question

UpStudy AI · Accepted Answer

The distance $$ AB $$ between points $$ A(1, 4) $$ and $$ B(7, 0) $$ can be calculated using the distance formula:

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

Substituting the given coordinates:

$$
AB = \sqrt{(7 - 1)^2 + (0 - 4)^2} = \sqrt{6^2 + (-4)^2} = \sqrt{36 + 16} = \sqrt{52} = 2\sqrt{13}
$$

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

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