Chapter 1, Problem 17RP

Solution

a.

The coordinate of C

The coordinate of C is $-3$

Given: C is the mid-point of BD

Concept used: Here, we let $x=-8$ and $y=2$

We are using mid-point formula which is $\frac{x+y}{2}$

Calculation: Here, the formula is $\frac{x+y}{2}$

By putting the values of x and y in the given formula, we get

→ $\frac{-8+2}{2}$

→ $\frac{-6}{2}$

→ $-3$

Conclusion: Hence, the coordinate of C is $-3$

b.

To find the coordinate of A

The coordinate of A is $-13$

Given: The length of AD is 15

Concept used: Here, we are using distance formula

  $AD=\sqrt{{\left(D-A\right)}^2}$

Calculation: Here, $AD=15$ and $D=2$ . Now putting these values in the above equation

→ $15=\sqrt{{\left(2-A\right)}^2}$

→ $15=2-A$

→ $A=-13$

Conclusion: Hence, the value of the coordinate A is $-13$