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3 years ago

The coordinates of A are (0,4) and the x-coordinate of B is 5. What is the y-coordinate of B if AB=13?(Two answers are possible.

)
*could you give an explanation, i don't understand it but i know the possible answers which are 16 or -8*

Mathematics

1 answer:

Georgia [21]3 years ago

4 0

$\overline{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\
13=\sqrt{(5-0)^2+(y_B-4)^2}\\
13=\sqrt{25+y_B^2-8y_B+16}\\
13=\sqrt{y_B^2-8y_B+41}\\
169=y_B^2-8y_B+41\\
y_B^2-8y_B-128=0\\
y_B^2+8y_B-16y_B-128=0\\
y_B(y_B+8)-16(y_B+8)=0\\
(y_B-16)(y_B+8)=0\\
y_B=16 \vee y_B=-8
$

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