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# help with analytical geometry

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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 :)

Jan 14, 2024

#1
+36979
0

Yikes !

Jan 14, 2024
#2
+129803
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If I could figure this  out, I'd be qualified to fly the Space Shuttle.....

Jan 14, 2024