# Find the distance between the point (-3,4,-6)and its image in the XY plane. Pls answer fast..dont give any links..pls give explanation

If a point of an object has coordinates (x, y, z) then the image of this point (as reflected by a mirror in the xy plane) has coordinates (x, y, -z).
Hence the coordinate of the image of the point(-3,4,-6) in xy-plane will be (-3,4,6).
So the distance between them will be d = $\sqrt{\left({\mathrm{x}}_{2}-{\mathrm{x}}_{1}{\right)}^{2}+\left({\mathrm{y}}_{2}-{\mathrm{y}}_{1}{\right)}^{2}+\left({\mathrm{z}}_{2}-{\mathrm{z}}_{1}{\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{{\left(-3+3\right)}^{2}+{\left(4-4\right)}^{2}+{\left(6+6\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{\left(6+6{\right)}^{2}}\phantom{\rule{0ex}{0ex}}=12$

• 0
What are you looking for?