Question

Cuantas unidades mide el lado QR? cual es la distancia entre los puntos P y R​

Answer 1

Part A)
`QR=2√(5)\ units`

Part B)
`PR=2√(13)\ units`

Explanation:

The complete question in English is

Observe the isosceles PQRS trapeze in the Cartesian plane.

A) How long is the QR side?

B) What is the distance between points P and R?

The picture of the question in the attached figure

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Part A) How long is the QR side?

we have the coordinates

Q(7,6) and R(9,2)

substitute in the formula

`d=\sqrt{(2-6)^(2)+(9-7)^(2)}`

`d=\sqrt{(-4)^(2)+(2)^(2)}`

`d_Q_R=√(20)\ units`

simplify

`d_Q_R=2√(5)\ units`

Part B) What is the distance between points P and R?

we have the coordinates

P(3,6) and R(9,2)

substitute in the formula

`d=\sqrt{(2-6)^(2)+(9-3)^(2)}`

`d=\sqrt{(-4)^(2)+(6)^(2)}`

`d_P_R=√(52)\ units`

simplify

`d_P_R=2√(13)\ units`