Question

A (8,2)
B (6,4)
C (8,10)

Luella drew the triangle shown on a coordinate grid. To find the triangle's area, she multiples 1/2 by 2 and then multiples the result by another number. What is the number Luella can use to compete the calculation?

Luella can multiply 1/2 by 2 by _ to find the triangle's area.

Answer 1

To find the area of a triangle given its vertices at points A (8, 2), B (6, 4), and C (8, 10), you can use the formula for the area based on the coordinates of the vertices.

The formula for the area of a triangle given vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is:

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

Substituting the points A (8, 2), B (6, 4), and C (8, 10):

- For \(A (x_1, y_1) = (8, 2)\)
- For \(B (x_2, y_2) = (6, 4)\)
- For \(C (x_3, y_3) = (8, 10)\)

Now we can substitute into the formula:

\[
\text{Area} = \frac{1}{2} \left| 8(4-10) + 6(10-2) + 8(2-4) \right|
\]
\[
= \frac{1}{2} \left| 8(-6) + 6(8) + 8(-2) \right|
\]
\[
= \frac{1}{2} \left| -48 + 48 - 16 \right|
\]
\[
= \frac{1}{2} \left| -16 \right|
\]
\[
= \frac{1}{2} \times 16
\]
\[
= 8
\]

So, Luella's full calculation to find the area involves multiplying \( \frac{1}{2} \) by \( 2 \) and then by \( 8 \):

\[
\text{Area} = \frac{1}{2} \times 2 \times 8
\]

Thus, the number Luella can multiply \( \frac{1}{2} \) by \( 2 \) to find the triangle's area is:

**8**