Can someone please help me I'm very stuck geometry isn't my thing

1. (10, -⁸/₃)

2. (2, ⁸/₃)

3. (12, -4)

Step-by-step explanation:

I will do the first 3 as examples.

1. Y is ⅔ of the distance from X to Z.

Y − X = ⅔ (Z − X)

The x-coordinate of Y is:

x − -6 = ⅔ (18 − -6)

x + 6 = ⅔ (24)

x + 6 = 16

x = 10

The y-coordinate of Y is:

y − 8 = ⅔ (-8 − 8)

y − 8 = ⅔ (-16)

y − 8 = -³²/₃

y = -⁸/₃

Y is at (10, -⁸/₃).

2. The ratio of XY to YZ is 1:2.

(Y − X) / (Z − Y) = 1 / 2

Cross multiply.

2 (Y − X) = Z − Y

The x-coordinate of Y is:

2 (x − -6) = 18 − x

2x + 12 = 18 − x

3x = 6

x = 2

The y-coordinate of Y is:

2 (y − 8) = -8 − y

2y − 16 = -8 − y

3y = 8

y = ⁸/₃

Y is at (2, ⁸/₃).

3. Y is ¼ of the distance from Z to X.

Y − Z = ¼ (X − Z)

The x-coordinate of Y is:

x − 18 = ¼ (-6 − 18)

x − 18 = ¼ (-24)

x − 18 = -6

x = 12

The y-coordinate of Y is:

y − -8 = ¼ (8 − -8)

y + 8 = ¼ (16)

y + 8 = 4

y = -4

Y is at (12, -4).

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.