Question

if AB = 5.
Given A = (x + 2, -2) and B = (11, 6). Find
x if AB = 17.
.
2 1) Find​

Answer 1

Answer

24 and -6

Step-by-step explanation

Note:-

• If A(a,b) and B(c,d) are two points , the the distance between them, AB is given by ,
• AB = $\sqrt{{(a-c)}^{2}+{(b-d)}^{2}}$

Solution:-

• Given, A = (x+2 , -2) B = (11,6) Comparing to the above formula,
• a = x+2
• b = -2
• c = 11
• d = 6
• AB = 17
• Substitute the values in the formula

AB = $\sqrt{{(a-c)}^{2}+{(b-d)}^{2}}$

${AB}^{2}$ = ${(a-c)}^{2}+{(b-d)}^{2}$

${17}^{2}$ = ${(x+2-11)}^{2}+{(-2-6)}^{2}$

289 = ${(x-9)}^{2}+{(-8)}^{2}$

289 = ${x}^{2}+81-18x+64$

289 = ${x}^{2}+81-18x+64$

${x}^{2}-18x-144$ = 0

${x}^{2}+6x-24x-144$ = 0

x(x+6)-24(x+6) = 0

(x-24)(x+6) = 0

x-24 = 0 => x = 24

x+6 = 0 => x = -6

The values of x are 24 and -6