Question

Show that (0,7,-10), (1,6,-6) and (4,9,-6) are the vertices of an isosceles triangle

Answer 1

Answer:

Plot simply on graph you will get a isocelles triangle

Check by measuring angles and sides.

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

${\boxed{\sf\:{Points\;be\;PQR}}}$

Hence,

PQ = √{(1 - 0)² + (6 - 7)² + (-6 + 10)²}

PQ = √{(1)² + (-1)² + (4)²}

PQ = √(1 + 1 + 16)

PQ = √18

PQ = 3√2

$\textbf{\underline{Here\;we\;get:-}}$

PQ = 3√2

Now,

QR = √{(4 - 1)² + (9 - 6)² + (-6 - 6)²}

QR = √{(3)² + (3)²}

QR = √(9 + 9)

QR = √18

QR = 3√2

$\textbf{\underline{Here\;we\;get:-}}$

QR = 3√2

Now,

RP = √{(0 - 4)² + (7 - 9)² + (-10 + 6)²}

RP = √{(-4)² + (-2)² + (-4)²}

RP = √(16 + 4 + 16)

RP = √(20 + 16)

RP = √36

RP = 6

$\textbf{\underline{Here\;we\;get:-}}$

RP = 6

Therefore we get,

PQ = QR ≠ RP

$\Large{\boxed{\sf\:{We\;observed\;that\;points\;are\; vertices\;of\;isosceles\;triangle}}}$