Question

Considerando que um ponto do eixo das ordenadas tem a mesma distância de (-2,1) e (4,-1), determine as coordenadas desse ponto.

Answer 1

$∣AC∣=∣BC∣</p><p></p><p>AC=C-A=(0;y)-(-2;1)=(2;y-1)AC=C−A=(0;y)−(−2;1)=(2;y−1)</p><p></p><p>|AC|=\sqrt{2^2+(y-1)^2}=\sqrt{4+y^2-2y+1}∣AC∣=22+(y−1)2=4+y2−2y+1</p><p></p><p>BC=C-B=(0;y)-(4;-1)=(-4;y+1)BC=C−B=(0;y)−(4;−1)=(−4;y+1)</p><p></p><p>|BC|=\sqrt{(-4)^2+(y+1)^2}=\sqrt{16+y^2+2y+1}∣BC∣=(−4)2+(y+1)2=16+y2+2y+1</p><p></p><p>|AC|=|BC|∣AC∣=∣BC∣ < = ><=></p><p></p><p>< = > \sqrt{4+y^2-2y+1}=\sqrt{16+y^2+2y+1} < = ><=>4+y2−2y+1=16+y2+2y+1<=></p><p></p><p>< = > y^2-2y+5=y^2+2y+17 < = ><=>y2−2y+5=y2+2y+17<=></p><p></p><p>< = > y^2-y^2-2y-2y+5-17=0 < = ><=>y2−y2−2y−2y+5−17=0<=></p><p></p><p>< = > -4y=12 < = ><=>−4y=12<=></p><p></p><p>< = > y=-\frac{12}{4} < = ><=>y=−412<=></p><p></p><p>< = > y=-3<=>y=−3$