. A point P is equidistant from R(-2, 4) and S(6,-4) and its x-coordinate is twice its y-coordinate.
(0) Find the coordinates of P.
(ii) Hence, determine whether P, R and S are
collinear, showing your working clearly.​

I) coordinate of P is (11, 5.5)

II) Points are not collinear

Step-by-step explanation:

I) Let the coordinates of P be (a, b)

We are told that its x-coordinate is twice its y-coordinate. Thus, a = 2b

Now, P is equidistant from R(-2, 4) and S(6,-4). Thus;

PR = PS

Using the formula for distance between two coordinates, we have;

√((a - (-2))² + (b - 4)²) = √((a - 6)² + (b - (-4))²)

This gives;

(a + 2)² + (b - 4)² = (a - 6)² + (b + 4)²

Since a = 2b,then we have;

(2b + 2)² + (b - 4)² = (2b - 6)² + (b + 4)²

4b² + 8b + 4 + b² - 8b + 16 = 4b² - 12b + 36 + b² + 8b + 16

Simplifying this gives;

20 = 42 - 4b

42 - 20 = 4b

4b = 22

b = 22/4

b = 11/2

b = 5.5

Since a = 2b

Then a = 2 × 5.5

a = 11

Thus, coordinate of P is (11, 5.5)

II) Formula for area of triangle formed by three points is given as;

A = ½|(x1 - x2) (x2 - x3)|

|(y1 - y2) (y2 - y3)|

x1 - x2 = 11 - (-2) = 13

x2 - x3 = -2 - 6 = -8

y1 - y2 = 5.5 - 4 = 1.5

y2 - y3 = 4 - (-4) = 8

Thus;

A = ½|13 -8|

|1.5 8|

A = ½((13 × 8) - (1.5 × - 8))

A = ½(104 + 12)

A = 58

Since the area is not zero, then it means the points are not collinear.

the answer is b. 60. each interior angle in 120, so the exterior angle must be 60 in order to add up to 180

step-by-step explanation:

its a lot blury