Question

Just ignore question 7

Answer 1

AB = 9.22 units

BC = 8.60 units

AC = 7.28 units

Perimeter = 25.10 units

Explanation:

Given triangular points:

• A(-4,4)
• B(5,2)
• C(-2,-3)

To find:

• AB =
• BC =
• AC =
• Perimeter

Solution:

In order to find the perimeter of the triangle, we need to add all the sides.

To find the lengths of the sides, we can use the distance formula:

`\boxed{\boxed{\sf d = √((x_2 - x_1)^2 + (y_2 - y_1)^2) }}`

Using this formula, we can find the following:

`\sf AB = √((5 - (-4))^2 + (2 - 4)^2) \\\\ = √( (5+4)^2 + (-2)^2 )\\\\ = √((9)^2 +(-2)^2 ) \\\\ = √( 81+4)\\\\ = √(85) \\\\ = 9.2195444572928 \\\\ \approx 9.22 \textsf{( in 2 d.p.)}`

`\sf BC = √((-2 - 5)^2 + (-3 - 2)^2) \\\\ = √((-7)^2 +(-5)^2)\\\\ = √(49+ 25) \\\\ = √(74) \\\\ = 8.6023252670426\\\\ \approx 8.60 \textsf{( in 2 d.p.)}`

`\sf AC = √((-2 - (-4))^2 + (-3 - 4)^2) \\\\ =√((-2+4)^2 + (-7)^2 )\\\\ =√((2)^2 +(-7)^2 ) \\\\ √(4+ 49) \\\\= √(53) \\\\ = 7.2801098892805\\\\ \approx 7.28 \textsf{( in 2 d.p.)}`

Therefore, the perimeter of the triangle is:

Perimeter = AB + BC + AC

= 9.22 + 8.60 + 7.28

= 25.10 units

So, the final answer are:

AB = 9.22 units

BC = 8.60 units

AC = 7.28 units

Perimeter = 25.10 units