Answer:
M = (8 ; -5)
Step-by-step explanation:
R = ( 13; -10)
M = (x ; y)
S = (3 ; 0 )
|___________|___________|
R (13;-10) M (x;y) S ( 3; 0)
So:
dRM = dMS
√[(y - (-10))^2 + (x - 13)^2] = √[(0 - y)^2 + (3 - x)^2]
(y + 10)^2 + (x - 13)^2 = (0 - y)^2 + (3 - x)^2
y^2 + 20*y + 100 + x^2 - 26*x + 169 = (- y)^2 + 9 - 6*x + x^2
y^2 + 20*y + 100 + x^2 - 26*x + 169 = y^2 + 9 - 6*x + x^2
20*y - 26*x + 269 = 9 - 6*x
20*y - 20*x = - 260
20*(y - x) = - 260
x - y = 13
x - 13 = y
Also:
2*dMS = dRS
2*√[(0 - y)^2 + (3 - x)^2] = √[(0 - (-10))^2 + (3 - 13)^2]
4*[(- y)^2 + (3 - x)^2] = [10^2 + (-10)^2]
4*[y^2 + 9 - 6*x + x^2] = 100 + 100
y^2 + 9 - 6*x + x^2 = 200 / 4
y^2 + 9 - 6*x + x^2 = 50
y^2 + x^2 - 6*x = 41
(x - 13)^2 + x^2 - 6*x = 41
x^2 - 26*x + 169 + x^2 - 6*x = 41
2*x^2 - 32*x + 128 = 0
x^2 - 16*x + 64 = 0
(x - 8)^2 = 0
x - 8 = 0
x = 8
Thus:
x - 13 = y
8 - 13 = y
- 5 = y
⇒ M = (8 ; -5)
