Question

Luella drew the triangle shown on a coordinate grid. To find the triangle's area, she multiplies 1/2 by 2 and then multiplies the result by another number. What is the number Luella can use to complete the calculation?
Point A: (8, 2)
Point B: (6, 4)
Point C: (8, 10)

Answer 1

To find the area of a triangle given its vertices on a coordinate grid, we can use the formula derived from the coordinates of the vertices, which is:

\[
\text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right|
\]

For points A (8, 2), B (6, 4), and C (8, 10), we assign the coordinates as follows:
- \( (x_1, y_1) = (8, 2) \)
- \( (x_2, y_2) = (6, 4) \)
- \( (x_3, y_3) = (8, 10) \)

Now, substituting these values into the area formula:

\[
\text{Area} = \frac{1}{2} \left| 8(4-10) + 6(10-2) + 8(2-4) \right|
\]

Calculating inside the absolute value:

1. \( 8(4-10) = 8(-6) = -48 \)
2. \( 6(10-2) = 6(8) = 48 \)
3. \( 8(2-4) = 8(-2) = -16 \)

Combining these results:

\[
-48 + 48 - 16 = -16
\]

Now putting it back into the area formula:

\[
\text{Area} = \frac{1}{2} \left| -16 \right| = \frac{1}{2} \times 16 = 8
\]

Since Luella multiplies \( \frac{1}{2} \) by \( 2 \) first, that means she is focusing on the term:

\[
\frac{1}{2} \times 2 = 1
\]

To complete the calculation to find the area, we need the last number:

\[
\text{Area} = 1 \times 8 = 8
\]

So the number Luella can use to complete the calculation is:

\[
\boxed{8}
\]