Question

find the value of Y if the distance between point A(2, -2) and N (-1,Y) is 5​

Answer 1

Step-by-step explanation:

Using distance formula,

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

$\sqrt{ {( - 1 - 2)}^{2} + (y + 2) ^{2} } = 5$

Squaring both sides,

${ ( - 3)}^{2} + (y + 2) ^{2} = 25$

$9 + {y}^{2} + 4y + 4 = 25$

${y}^{2} - 4y = 25 - 9 - 4$

${y}^{2} - 4y - 12 = 0$

${y }^{2} - 6y + 2y - 12 = 0$

$y(y - 6) + 2(y - 6)$

$(y + 2)(y - 6) = 0$

$either \: y = 6 \: or \: y = - 2 \: units$