Triangle ABC is reflected over the x-axis and then translated eight units right to form triangle GHI. The length of side BC, in units, is shown.

Question

Triangle A-B-C has its vertex A at (-7, 5), B at (-7, 3), C at (-3, 3). Triangle G-H-I has vertex G at (1, -5), H at (1, -3) and vertex I is at (5, -3).

Enter the length, in units, of side HI.
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units

Answer 1

To find the length of side HI in triangle GHI, we first need to determine the coordinates of points H and I.

The coordinates of point H are given as \((1, -3)\) and the coordinates of point I are given as \((5, -3)\).

Now, to calculate the length of segment HI, we can use the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

In our case:

• Point H: \((x_1, y_1) = (1, -3)\)
• Point I: \((x_2, y_2) = (5, -3)\)

Now we plug in the values into the distance formula:

\[ d = \sqrt{(5 - 1)^2 + (-3 - (-3))^2} \]

Calculating the differences:

\[ d = \sqrt{(4)^2 + (0)^2} = \sqrt{16 + 0} = \sqrt{16} = 4 \]

Thus, the length of side HI is:

\[ \boxed{4} \text{ units} \]