Question

Can you help with this please.

Answer 1

8.1 units

Explanation:

Distance Formula

• d = √(x₂ - x₁)² + (y₂ - y₁)²

Solving

• d = √(14 - 10)² + (12 - 5)²
• d = √4² + 7²
• d = √65
• d = 8.1 units (nearest tenth)

Answer 2

`\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}`

• Given - two points P ( 5 , 10 ) and R ( 12 , 14 ) on the cartesian plane

• To find - distance between the two points

Using the distance formula ~

`\qquad\underline{d(PR) = \sqrt{( x_(2) - x_(1)) {}^(2) + ( y_(2) - y_(1)) {}^(2) }} \\ \\`

we have ,

`\longrightarrow x_(1) = 5 \\ \longrightarrow x_(2) = 12 \\ \\ \longrightarrow \: y_(1) = 10 \\ \longrightarrow \: y_(2) = 14`

substituting the values in the formula , we get

`d(PR) = \sqrt{(12-5) {}^(2) + (14-10) {}^(2) } \\ \\ \implies \: d(PR) = \sqrt{(7) {}^(2) + ( 4) {}^(2) } \\ \\ \implies \: d(PR) = √(49 + 16) \\ \\ \implies \: d(PR) = √(65) \\ \\ \implies \: d(PR) = 8.1 \: units \: (approx)`

hope helpful :)