Question

Find the distance between the points (9, –6) and (–4, 7). Question 15 options: A) B) C) D)

Answer 1

o find the distance between the points (9, -6) and (-4, 7), we can use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case,

(

�

1

,

�

1

)

=

(

9

,

−

6

)

(x

1

​

,y

1

​

)=(9,−6) and

(

�

2

,

�

2

)

=

(

−

4

,

7

)

(x

2

​

,y

2

​

)=(−4,7).

Plugging these values into the distance formula:

Distance = √((-4 - 9)² + (7 - (-6))²)

Distance = √((-13)² + (7 + 6)²)

Distance = √(169 + 169)

Distance = √(338)

To simplify the square root, we can express 338 as a product of its prime factors:

338 = 2 × 13 × 13

Now, we can take the square root:

Distance = √(2 × 13 × 13)

Since the square root of a product is equal to the product of the square roots of the factors, we get:

Distance = √2 × √(13 × 13)

Distance = √2 × 13

So, the distance between the points (9, -6) and (-4, 7) is 13√2 units.

The correct answer is D)

13

√

2

13√2.

D)

rhombus.

planation:

Answer 2

`\huge \boxed{ \boxed{ \tt √(170) }}`

Explanation:

to understand this

you need to know about:

• coordinates
• PEMDAS

given:

• point:(9,-6),(-4,7)

tips and formulas:

• 
  `d = \sqrt{(x _(2) - x _(1) ) ^(2) + (y_(2) - y_1 {)}^(2) } \atop`

let's solve:

1. 
   `\sf substitute \: the \: value \: o f \:x _(2) \: x _(1) \: y_(2) \: y_1 \: respectively : \\ \sqrt{(9-(-4) ) ^(2) + (-6 - (-7){)}^(2) }`
2. 
   `\sf simplify : \\ \sqrt{(9-(-4) ) ^(2) + (-6 - (-7){)}^(2) } \\ \sqrt{(9 + 4 {)}^(2) + ( - 6 + 7 {)}^(2) } \\ \sqrt{ {13}^(2) + {1}^(2) } \\ √(169 + 1) \\ √(170) \\`