Question

HELP PLS WILL GIVE BRAIN
Drag each expression to the correct location on the graph and equation. Not all expressions will be used
Complete the given diagram by dragging expressions to each leg of the triangle. Then correctly complete the equation to derive the distance.

Answer 1

Answer:

This is the distance formula

(x₂ - x₁)² + (y₂ - y₁)² = d²

complete the equation to derive the distance.

(2 - -3)² + (-4 - 3)² = d²

5² + (-7)² = d²

25 + 49 = d²

64 = d²

d = 8

Answer 2

$AC= d = (x_{2} -x_{1}) ^{2} + (y_{2} -y_{1}) ^{2}$

$BC = (y_{2} -y_{1} )$

$AB = (x_{2} -x_{1} )$

What is the length of a line segment?

The distance between two points is called the length of the line segment.

Distance formula

$\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2} -y_{1} )^{2} } =d$

Where,

d is the distance between the two points

$(x_{1},x_{2}) and (y_{1},y_{2})$ are the two points

What is Pythagoras theorem?

It states that "the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)".

According to the given question

We have a graph of a triangle ABC

Length of AC  is d.

Coordinates of A is $(x_{1},y_{1})$

Coordinates of B  is $(2, 3)$

and coordinates of C is $(x_{2}, y_{2} )$

Now, according to the distance formula, length of AC is given by

$AC = d =\sqrt{(x_{2}-x_{1} ) ^{2}+(y_{2}-y_{1}) ^{2} }$

⇒ $d = (x_{2} -x_{1}) ^{2} + (y_{2} -y_{1}) ^{2}$

By Pythagoras theorem and distance formula

$BC = (y_{2} -y_{1} )$

And, $AB = (x_{2} -x_{1} )$

Learn more about the distance formula and Pythagoras theorem here:

https://brainly.com/question/27801945

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