Question

Your house is located at point T. Your grandma's house is located at point V. U is the midpoint of segment TV. How far do you need to travel to drive home from your grandma's house?

Answer 1

70

Explanation:

From the question given above, the following data were obtained:

TU = 8x + 11

UV = 12x – 1

Next, we shall determine the value of x.

From the question:

U is the midpoint. This means that TU and UV are equal i.e

TU = UV

With the above idea in mind, we shall determine the value of x as follow:

TU = UV

TU = 8x + 11

UV = 12x – 1

8x + 11 = 12x – 1

Collect like terms

11 + 1 = 12x – 8x

12 = 4x

Divide both side by the coefficient of x i.e 4

x = 12/4

x = 3

Next, we shall determine the length of TU and UV. This can be obtained as follow:

TU = 8x + 11

x = 3

TU = 8(3) + 11

TU = 24 + 11

TU = 35

UV = 12x – 1

x = 3

UV = 12(3) – 1

UV = 36 – 1

UV = 35

Finally we shall determine the length of TV. This can be obtained as follow:

TV = TU + UV

TU = 35

UV = 35

TV = 35 + 35

TV = 70

Therefore, the distance between my house and grandma's house is 70.

NOTE: Assume the distance is measured in kilometer (km)

This means that I will travel 70 km from grandma's house to my house.