Answer:
[tex]C = (1,0)[/tex]
[tex]E = (0.8,0)[/tex]
See attachment for C and E
Step-by-step explanation:
Given
[tex]O= (0,0)[/tex] --- Origin
[tex]CO = 1[/tex] --- distance of C to O
Solving (a): Plot point C
Calculate the coordinates of C using distance formula:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
Where:
[tex]O= (0,0)[/tex] ---[tex](x_1,y_1)[/tex]
[tex]C = (x,y)[/tex] -- [tex](x_2,y_2)[/tex]
[tex]d = CO = 1[/tex]
So, we have:
[tex]1 = \sqrt{(x - 0)^2 + (y -0)^2}[/tex]
[tex]1 = \sqrt{x^2 + y^2}[/tex]
Square both sides
[tex]1^2 = x^2 + y^2[/tex]
[tex]x^2 + y^2 =1[/tex]
For this solution, we assume y = 0
[tex]x^2 + 0^2 =1[/tex]
[tex]x^2=1[/tex]
Solve for x
[tex]x = 1[/tex]
So, the coordinates of C is: (1,0)
[tex]C = (1,0)[/tex]
Solving (b): Plot point E
We have that E is 4/5 closer to the origin.
This implies that, the ratio is:
[tex]m : n = 4/5:1/5[/tex]
Multiply by 5
[tex]m : n = 4:1[/tex]
So, E is at 4:1 between O and C
Calculate the coordinates of E using:
[tex]E = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
Where
[tex]O= (0,0)[/tex] ---[tex](x_1,y_1)[/tex]
[tex]C = (1,0)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]m : n = 4:1[/tex]
[tex]E = (\frac{4*1 + 1 * 0}{4 + 1},\frac{4*0 + 1*0}{4 + 1})[/tex]
[tex]E = (\frac{4}{5},\frac{0}{5})[/tex]
[tex]E = (0.8,0)[/tex]
