Question

Given: AB- is a line segment with endpoints A(0, 6) and B(8, 0) and point M(4, 3).

Prove: AM- ≅ MB- using the distance formula.

Proof:
• First find the length of AM.
AM = √(x₂ − x₁)² + (Y₂ − y₁)²
= ____
= ____
= ____
= ____

• Next, find the length of MB.
MB = √(x₂ − x₁)² + (Y₂ − y₁)²
= ____
= ____
= ____
= ____

•AM- ≅ MB-​

Answer 1

To prove AM- and MB- are congruent, the distance formula is used to show both AM and MB have a length of 5 units, making them congruent.

Step-by-step explanation:

To prove that the line segments AM- and MB- are congruent using the distance formula, we will first calculate the length of each segment.

For AM, we use the endpoints A(0, 6) and M(4, 3):
AM = √((4 - 0)² + (3 - 6)²) = √(16 + 9) = √25 = 5

Next, for MB, we use the endpoints M(4, 3) and B(8, 0):
MB = √((8 - 4)² + (0 - 3)²) = √(16 + 9) = √25 = 5

Since both AM and MB have a length of 5 units, we conclude that AM- is congruent to MB-.

Answer 2

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{4}~,~\stackrel{y_2}{3})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ AM=√((~~4 - 0~~)^2 + (~~3 - 6~~)^2) \implies AM=√(( 4 )^2 + ( -3 )^2) \\\\\\ AM=√( 16 + 9 ) \implies AM=√( 25 )\implies \boxed{AM=5} \\\\[-0.35em] ~\dotfill`

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad B(\stackrel{x_2}{8}~,~\stackrel{y_2}{0})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ MB=√((~~8 - 4~~)^2 + (~~0 - 3~~)^2) \implies MB=√(( 4 )^2 + ( -3 )^2) \\\\\\ MB=√( 16 + 9 ) \implies MB=√( 25 )\implies \boxed{MB=5}`