What is the area of the composite figure whose vertices have the following coordinates?
1 answer:
Check the picture below.
notice, the composite is just a parallelogram, in blue, with a base of 6 units and a height of 4 units, and a triangle, in yellow, of a base of 6 units and a height of 2 units.
recall the area of a parallelogram is base*height, and for a triangle is (1/2)bh.
so, we can simply get the area of both and sum them up.
notice, the composite is just a parallelogram, in blue, with a base of 6 units and a height of 4 units, and a triangle, in yellow, of a base of 6 units and a height of 2 units.
recall the area of a parallelogram is base*height, and for a triangle is (1/2)bh.
so, we can simply get the area of both and sum them up.
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Answer:
Step-by-step explanation:
a = 2, b = 1, c = -3
We need to factor this by finding the product of a and c, then from there find which factors of a * c will either add or subtract to give us b.
a * c = 6 and the factors of 6 and 1 and 6, 2 and 3. Well, 6 - 1 doesn't equal 1 and neither does 6 + 1. So our factors are 3 and 2. In order to combine those to get a 1 (our b), we will subtract 2 from 3 since 3 - 2 = 1. That means that 3 is positive and 2 is negative. Filling in the formula with 3 and 2 in place of 1 looks like this (always remember to put the absolute value of the largest number first):
Group the first 2 terms together and the second 2 term together in order to factor:
and factor out what's common in each set of parenthesis.
Notice that when we factor out a -1 from the second set of parenthesis, we can distribute it back in to get the equation we started with. We know that factoring by grouping "works" if what is inside both sets of parenthesis is exactly the same. Ours are identical: (2x + 3). That is common now, and can be factored out:
That matches your first choice