Question

(Distance/midpoint formula) - triangle ABC has vertices on the coordinate plane at A(-6.3, 7.2) B(2.2, 4.4) and C(5.6, -3.4) find the length of BC.

Answer 1

8.51 units

Explanation:

Given:

`A(-6.3,7.2),B(2.2,4.4), C(5.6,-3.4)`

Length of BC can be obtained using distance formula.

For two points
`A(x_(1),y_(1))` and
`B(x_(2),y_(2))`, length of AB is given as:

`AB=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

Plug in 2.2 for
`x_(1)`, 4.4 for
`y_(1)`, 5.6 for
`x_(2)`, and -3.4 for
`y_(2)`. Solve for BC

`BC=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}\\ BC=\sqrt{(5.6-2.2)^(2)+(-3.4-4.4)^(2)}\\ BC=\sqrt{3.4^(2)+(-7.8)^(2)}=√(72.4)=8.51`

Therefore, the length of BC is 8.51 units.