Question

Plot c so its distance from the origin is 1. Plot poin e 4/5 closer to the origin than c. What is its cooridinate?

Answer 1

Answer:

$C = (1,0)$

$E = (0.8,0)$

See attachment for C and E

Step-by-step explanation:

Given

$O= (0,0)$ --- Origin

$CO = 1$ --- distance of C to O

Solving (a): Plot point C

Calculate the coordinates of C using distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}$

Where:

$O= (0,0)$ ---$(x_1,y_1)$

$C = (x,y)$ -- $(x_2,y_2)$

$d = CO = 1$

So, we have:

$1 = \sqrt{(x - 0)^2 + (y -0)^2}$

$1 = \sqrt{x^2 + y^2}$

Square both sides

$1^2 = x^2 + y^2$

$x^2 + y^2 =1$

For this solution, we assume y = 0

$x^2 + 0^2 =1$

$x^2=1$

Solve for x

$x = 1$

So, the coordinates of C is: (1,0)

$C = (1,0)$

Solving (b): Plot point E

We have that E is 4/5 closer to the origin.

This implies that, the ratio is:

$m : n = 4/5:1/5$

Multiply by 5

$m : n = 4:1$

So, E is at 4:1 between O and C

Calculate the coordinates of E using:

$E = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})$

Where

$O= (0,0)$ ---$(x_1,y_1)$

$C = (1,0)$ --- $(x_2,y_2)$

$m : n = 4:1$

$E = (\frac{4*1 + 1 * 0}{4 + 1},\frac{4*0 + 1*0}{4 + 1})$

$E = (\frac{4}{5},\frac{0}{5})$

$E = (0.8,0)$