Question

Show that points (1,7,), (4,2), (-1,-1),and(-4,4) are vertices of an isosceles triangle

Answer 1

Heymate here is ur answer

Vertices of the triangle are A(6,6), B(5,-2), C(7,-2)

Distance between two points = √(x2 - x1)2 + (y2 - y1)2

AB = √[(5 - 6)2 + (-2 -6)2] = √65

BC = √[(7 - 5)2 + (-2 -2)2] = √20

AC = √[(7 - 6)2 + (-2 -6)2] = √65 AB = AC Therefore, ΔABC is an isosceles triangle. Midpoint of the line segment joining (x1, y1) and (x2, y2) = [(x1 + x2)/2, (y1 + y2)/2]

Midpoint of BC = [(5 + 7)/2, (-2 -2)/2] = (6, -2) Length of the median from A = Distance between (6, 6) and (6, -2) = √[(6 - 6)2 + (-2 -6)2] = 8. Therefore, length of the median through A = 8 units.

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