Question

2. The distance between (-3, 2) and (x, -1) is square root of 45. Find x.

3. Show that the triangle with vertices (-1, 2), (-4, -1) and (3, -2) is a right triangle.

4. Show that the triangle with vertices (-10, 7), (-6, -2), and (3, 2) is isosceles
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Answer 1

2.

$d = \sqrt{45}$

$d = \sqrt{(x + 3) ^{2} + ( - 1 - 2) ^{2} }$

$45 = \sqrt{(x + 3)^{2} + 9}$

$45 = \sqrt{x ^{2} + 9 + 6x + 9}$

$45 = \sqrt{ {x}^{2} + 6x + 18 }$

$45^{2} = {x}^{2} + 6x + 18$

$2025 - 18 = {x}^{2} + 6x$

$2007 = x(x + 6)$

$x = 2007 \: or \: x + 6 = 2007 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 2001$