Question

ABC has A(-3,6),B(2,1),and C(9,5) as its vertices the length of side AB is units . The length of side BC is ?units . The length of side AC is ? Units .ABC ?

Answer 1

Answer:

The length of side AB is $\sqrt{50}$ units.

The length of side BC is $\sqrt{65}$ units.

The length of side AC is $\sqrt{145}$ units.

Step-by-step explanation:

To find the length of each side, we use the formula for the distance between two points.

Distance between two points:

Points $(x_1,y_1)$ and $(x_2,y_2)$. The distance between them is given by:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Side AB:

Points $A(-3,6),B(2,1)$. So the distance between them is:

$D = \sqrt{(2-(-3))^2 + (1-6)^2} = \sqrt{50}$

The length of side AB is $\sqrt{50}$ units.

Side BC:

Points $C(9,5),B(2,1)$. So the distance between them is:

$D = \sqrt{(2-9)^2 + (1-5)^2} = \sqrt{65}$

The length of side BC is $\sqrt{65}$ units.

Side AC:

Points $A(-3,6),C(9,5)$. So the distance between them is:

$D = \sqrt{(9-(-3))^2 + (5-6)^2} = \sqrt{145}$

The length of side AC is $\sqrt{145}$ units.