Question

Help please, wrong answers are reported

Answer 1

The second option, d = 9.9

Explanation:

To find the distance between points P(9, 8) and Q(2, 1) rounded to the nearest tenth, we will use the distance formula in the Cartesian coordinate system, which is derived from the Pythagorean theorem. The formula calculates the distance 'd' between two points P(x₁, y₁) and Q(x₂, y₂) as:

`\rightarrow d = √((x_2-x_1)^2+(y_2-y_1)^2)`

To proceed, we'll first identify the coordinates, in our case:

• 
  `(x_1, y_1)=(9,8)`
• 
  `(x_2, y_2)=(2,1)`

Then, we'll substitute these values into the distance formula:

`\Longrightarrow d = √((2-9)^2+(1-8)^2)\\\\\\\\\Longrightarrow d = √((-7)^2+(-7)^2)\\\\\\\\\Longrightarrow d = √(49+49)\\\\\\\\\Longrightarrow d = √(98)\\\\\\\\\Longrightarrow d = 7√(2)\\\\\\\\\therefore \boxed{d \approx 9.9}`

Thus, the second option is correct, d = 9.9.