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? (1 point) Luella can multiply 1/2 by 2 by to find the triangle’s area.
Point A 8, 2
Point B 6, 4
Point C 8, 10

Answer 1

To find the area of the triangle formed by points A(8, 2), B(6, 4), and C(8, 10) on a coordinate grid, we can use the formula for the area of a triangle given by its vertices:

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

Where the points are:
- \( (x_1, y_1) = A(8, 2) \)
- \( (x_2, y_2) = B(6, 4) \)
- \( (x_3, y_3) = C(8, 10) \)

Substituting in the coordinates:

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

Calculating each term:

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

Now substitute these values back into the area formula:

\[
\text{Area} = \frac{1}{2} \left| -48 + 48 - 16 \right|
\]
\[
\text{Area} = \frac{1}{2} \left| -16 \right| = \frac{1}{2} \times 16
\]
\[
\text{Area} = 8
\]

From the calculation above, we see that Luella multiplies \( \frac{1}{2} \) by \( 2 \) (which equals \( 1 \)) and then multiplies the result by \( 8 \).

Thus, the number Luella can use to complete the calculation is **8**.