Question

find the value of y if distance between two point (-2,3)and (10, y)is 19 cm

Answer 1

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Answer 2

We have been given the points (-2,3)and (10, y) and the distance between these two points is 19 cm.

We know the distance between two points is given by

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

We have,

$x_1=-2,y_1=3,x_2=10,y_2=y, d=19$

plugging these values in the above formula, we get

$19=\sqrt{(10+2)^2+(y-3)^2}$

$19=\sqrt{144+y^2-6y+9}$

$19=\sqrt{153+y^2-6y}$

Squaring both sides, we get

$361=153+y^2-6y\\ y^2-6y-208=0$

$y_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-208\right)}}{2\cdot \:1}$

$y=\frac{6\pm \sqrt{868}}{2\cdot \:1}$

$y_{1,2}=\frac{6\pm 2\sqrt{217}}{2}$

$y_{1,2}=3\pm \sqrt{217}$

Therefore, the value for y is given by

$y=3+\sqrt{217},\:y=3-\sqrt{217}$