Answer :

meerkat18
I think the figure is that of a right triangle.

Its short leg = 2 - 1 = 1 unit     This is the value of y.
Its long leg = 3 - 0 = 3 units    This is the value of x.

Use the Pythagorean theorem to solve for the hypotenuse.

a² + b² = c²
1² + 3² = c²
1 + 9 = c²
10 = c²
√10 = √c²
3.16 = c

The length of the hypotenuse is C.) 3.2   rounded to the nearest tenth.
calculista

we know that

the triangle ABC and triangle EDF are congruent triangles-----> given problem

therefore

[tex]AC=EF\\AB=ED\\BC=DF[/tex]

we know that

the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Step [tex]1[/tex]

Find the distance AB

[tex]A(0,1)\\B(0,2)[/tex]

substitute in the formula of the distance

[tex]d=\sqrt{(2-1)^{2}+(0-0)^{2}}[/tex]

[tex]d=\sqrt{(1)^{2}+(0)^{2}}[/tex]

[tex]dAB=1\ unit[/tex]

Step [tex]2[/tex]

Find the distance BC

[tex]B(0,2)\\C(3,2)[/tex]

substitute in the formula of the distance

[tex]d=\sqrt{(2-2)^{2}+(3-0)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(3)^{2}}[/tex]

[tex]dBC=3\ units[/tex]

Step [tex]3[/tex]

Find the distance AC

we know that

the triangle ABC is a right triangle

so

Applying the Pythagorean Theorem

[tex]AC^{2}=AB^{2} +BC^{2}[/tex]

substitute the values in the formula

[tex]AC^{2}=1^{2} +3^{2}[/tex]

[tex]AC=\sqrt{10}\ units=3.16\ units[/tex]

round to the nearest tenth

[tex]AC=3.2\ units[/tex]

therefore

[tex]EF=3.2\ units[/tex]

[tex]ED=1\ unit[/tex]

[tex]DF=3\ units[/tex]

the answer is

The length of the hypotenuse is equal to [tex]3.2\ units[/tex]

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