First slide

Cartesian plane

Question

The vertices of $Δ O A B$ are $O (0, 0), A (0, 8), B (8, 0)$ . Then the length of the altitude from $O$ is

Moderate

A

$4 \sqrt{2}$
B

$7 \sqrt{2}$
C

$\frac{7}{2 \sqrt{2}}$
D

$\frac{7}{\sqrt{2}}$

Solution

$O (0, 0), A (0, 8), B (8, 0)$
$O A = O B = 8$

$Δ O A B$ in isosceles .

Midpoint of $A B = (4, 4)$

$∴$ Altitude through A = median $O D = \sqrt{16 + 16} = \sqrt{32} = 4 \sqrt{2}$

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