Luella drew the triangle shown on a coordinate grid. To find the triangle’s area, she multiplies 12 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 12 by 2 by to find the triangle’s area.

Question

a(8,2)
b(6,4)
c(8,10)

Answer 1

To find the area of a triangle on a coordinate grid, we can use the formula:

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

Given that Luella multiplies 12 by 2 first, it seems she is computing the area using one of the triangle’s dimensions as follows:

First, letting the base \( b \) equal 12 and then the height \( h \) equal 2, we can rewrite the area formula as:

\[ \text{Area} = \frac{1}{2} \times 12 \times 2 \]

Now, let's find out what this area would actually equal:

\[ \text{Area} = \frac{1}{2} \times 12 \times 2 = \frac{1}{2} \times 24 = 12 \]

The value that Luella would multiply this result (12) by to find out the area if she were indeed considering a triangle corresponding to the identified points could come from calculating the base and height from those points.

Let’s break down the coordinates:

• Point A: (8, 2)
• Point B: (6, 4)
• Point C: (8, 10)

We can check for the base and height based on the y-values of these points. Only two points need to form a vertical distance and a horizontal distance.

After calculating the vertex relationships:

1. Use points A and C (8, 2) and (8, 10):
   • The base (horizontal distance) between A and C has no x-distance since \( x \) is constant at 8.
   • The height (vertical distance) is the different y-values \( 10 - 2 = 8 \).

However, if we are indeed looking to resolve something other than the straightforward height calculation, we should measure distance considering the effective base.

So:

• If A and B formed a base using \( y \) then; 8 for base and 4 for the height could give area.

Given the calculation structure by Luella:

1. The triangle's area's correctness would thus stem from consolidating that:

Thus the choice made from verifying the base calculated would indeed yield effective overall structure via further operation on base height evaluating the overall using fractions.

In summary:

• The number mechanic for Luella to finalize would be: \( \frac{1}{2} \) to accompany the already multiplied 24 = area 12.

Therefore, the number Luella can multiply by to finalize the area of the triangle is \(\frac{1}{2}\) or 0.5 to validate the area finalization through traditional means and this directly leads to the utilized vertex points effectively resolving the core values of height.

Thus, any further question elucidated would revolve around proper geometric interpretations directly linked from the height operated based on these effective quadrants.