Determine if the triangles are similar \triangle LNM\sim \triangle

Find the point on the line $y=2x+3$ that is closest to the origin.

Let ${\displaystyle Q^2}$ be the rational plane of all ordered pairs (x,y) of rational numbers with the usual interpretations of the undefined geometric terms used in analytical geometry. Show that axiom C-1 and the elementary continuity principle fail in ${\displaystyle Q^2}$. (Hint: the segment from (0,0) to (1,1) can not be laid off on the x axis from the origin.
Axiom C-1: If A, B are two points on a line a, and if A' is a point upon the same or another line a′ , then, upon a given side of A′ on the straight line a′ , we can always find a point B′ so that the segment AB is congruent to the segment A′B′ . We indicate this relation by writing ${\displaystyle AB\stackrel{\sim }{=}A\prime B\prime }$. Every segment is congruent to itself; that is, we always have ${\displaystyle AB\stackrel{\sim }{=}AB}$.

Distance between (5,-6,4) and (-2,2,6)?

Solve the following systems of congruences.
$2x\equiv 5(mod3)$
$3x+2\equiv 3(mod8)$
$5x+4\equiv 5(mod7)$

Let quadrilateral ABCD satisfy $\mathrm{\angle }BAC=\mathrm{\angle }CAD=2\mathrm{\angle }ACD={40}^{\circ }$ and $\mathrm{\angle }ACB={70}^{\circ }$. Find $\mathrm{\angle }ADB$.

Find the equation of the ellipse
${\displaystyle x^2+9y^2-4x-72y+139=0}$
and locate the coordinates of the foci.