+4 hi, sorry, I wasn't able to attend class and need some help with two questions that I'm struggling with.
1. Point is reflected over the line shown below to point B. Find the coordinates of B.
[asy]
usepackage("amsmath");
usepackage("amssymb");
unitsize(0.6 cm);
pair M, P, Q;
P = (5,1);
Q = reflect((0,2), (2,3))*(P);
M = (P + Q)/2;
draw((-1,0)--(6,0));
draw((0,-1)--(0,7));
draw(P--Q,dashed);
draw((-1,1/2*(-1) + 2)--(6,6/2 + 2));
label("$x$", (6,0), SE);
label("$y$", (0,7), NE);
dot("$A = (7,1)$", P, S);
dot("$B$", Q, N);
//dot("$M$", M, S);
label("$y = \dfrac{1}{2} x + 4$", (6,6/2 + 2), E);
[/asy]
2. Line l is drawn in the coordinate plane below. If the slope of line l is 2 then find the area of the triangle determined by the line and the coordinate axes.
[asy]
unitsize(1 cm);
pair A, B, O, P;
A = (2,0);
B = (0,-3);
O = (0,0);
P = (O + reflect(A,B)*(O))/2;
draw(interp(A,B,-0.2)--interp(A,B,1.2), blue);
draw((-1,0)--(3,0));
draw((0,-4)--(0,1));
draw(O--P);
draw(rightanglemark(O,P,B,5));
label("$x$", (3,0), E);
label("$y$", (0,1), N);
label("$\ell$", interp(A,B,-0.2), N);
label("$3$", (O + P)/2, SW, red);
[/asy]
any help would be much appreciated :)
