Show that the points are vertices of an isosceles triangle?

Use the distance formula for each pair of points:

d = SQR[(x2 - x1)^2 + (y2 - y1)^2]

If you find that two of the distances are the same, the triangle formed by the three points is isosceles by definition.

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in case you be conscious of the gap formula in 2-dimesions.....d=sqrt[(X2-X1)^2+(Y2-Y... in basic terms enhance it to 3 dimensions........d=sqrt[(X2-X1)^2+(Y2-Y... PQ:::d=sqrt9=3 PR:::d=sqrt2 QR:::d=sqrt9=3 Triangle is isosceles

Find the distances between points A, B, and C,

to get side AB, side BC, and side AC.

If two sides are equal then it's isosceles.

For side AB:  A = (Ax, Ay) = (2, 3)   and   B = (Bx, By) = (4, 9)

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    side AB = √  [ (Bx – Ax)² + (By – Ay)²   ]