Chapter 2, Problem 20RP

a.

To determine

The coordinates of B and D

Answer to Problem 20RP

The coordinate of B is $\left(0,8\right)$ and D is $\left(6,-5\right)$

Explanation of Solution

Given: ABCD is a rectangle

Calculation: Here, $C\left(6,8\right)$ is given

And point B is on y-axis with no x-axis.

So, ABCD is a rectangle then, B $\left(0,8\right)$

Same for coordinate D

So that, D $\left(6,-5\right)$

Conclusion: Hence, the coordinate of B is $\left(0,8\right)$ and D is $\left(6,-5\right)$

b.

To determine

Probability that selected point is in the shaded region.

Answer to Problem 20RP

Probability that selected point is in the shaded region is $0.38$

Explanation of Solution

Given: Point is within ABCD

Concept used: Here, we are using formula of probability which is

  →$\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

Calculation: Here, the formula is $\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$ ................. $\left(1\right)$

AO = $\sqrt{25}$ and AD = $\sqrt{36+0}$

→ AO = 5 and AD = 6

So that, area of AOED = $6\times 5$ = $30$

And, AB = $\sqrt{{13}^2}$

→AB = 13 and AD = 6

So, area of ABCD = $13\times 6=78$

So that, here favorable outcomes are $30$ and total outcomes are 78

Now, putting these values in equation $\left(1\right)$

  →$\frac{30}{78}$

  →$0.38$

Conclusion: Hence, Probability that selected point is in the shaded region is $0.38$