Question

What is the area of a triangle with vertices at (−4, 1) , ​ (−7, 5) ​ , and ​ (0, 1) ​ ? Enter your answer in the box. ___units²

Answer 1

Check the picture below.

you can pretty much count those lengths off the grid.

recall that A = 1/2 bh.

Answer 2

Since area (a) of a triangle = 1/2 (b)*(h), our base will be the horizontal distance between (-4, 1) and (0, 1), which is just the absolute (positive) value of the difference between the x-values:
$| - 4 - 0| = 4$
So b = 4 units
Now the height is the vertical distance from top to bottom, or the absolute value of the difference between y-values:
$|5 - 1 | = 4$
So h = 4
Now a = 1/2 (b)(h) = 1/2 (4)(4) = 1/2 (16) = 8 units squared...
$answer = 8 {units}^{2}$