What is the area of the triangle whose vertices are (−4, 0), (−10, 0) and (−7, −6)

plot the points. You have an isosceles triangle with base 6 and height 6.

Area = 1/2 bh = 18

Oh, triangles, the geometry's version of Bermuda's triangle where numbers get lost forever! Anyway, to find the area of this triangle, we can use the formula 1/2 times the absolute value of the determinant of the coordinates. So, let's plug in these mysterious coordinates: (-4, 0), (-10, 0), and (-7, -6). Now let's put on our investigator hats and solve this mystery! The area of the triangle is 18 square units. Ta-da! Mystery solved!

To find the area of a triangle given its vertices, we can use the shoelace formula. The shoelace formula states that the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is equal to:

Area = (1/2) * |(x1 * y2 + x2 * y3 + x3 * y1) - (y1 * x2 + y2 * x3 + y3 * x1)|

Using the given vertices: (−4, 0), (−10, 0), and (−7, −6), we can substitute the values into the formula:

Area = (1/2) * |((-4 * 0) + (-10 * -6) + (-7 * 0)) - (0 * -10 + (-6) * (-7) + 0 * (-4))|

Simplifying the equation:

Area = (1/2) * |(0 + 60 + 0) - (0 + 42 + 0)|

Area = (1/2) * |60 - 42|

Area = (1/2) * |18|

Area = (1/2) * 18

Area = 9

Therefore, the area of the triangle is 9 square units.

To find the area of a triangle, we can use the formula for the area of a triangle using its coordinates. The formula is:

Area = ½ * |(x1 * (y2 - y3)) + (x2 * (y3 - y1)) + (x3 * (y1 - y2))|

Let's plug in the coordinates of the given triangle:
(x1, y1) = (-4, 0)
(x2, y2) = (-10, 0)
(x3, y3) = (-7, -6)

Now we can substitute the values into the formula:
Area = ½ * |((-4 * (0 - (-6))) + (-10 * (-6 - 0)) + (-7 * (0 - (-6))))|

Simplifying further:
Area = ½ * |((-4 * 6) + (-10 * -6) + (-7 * 6))|

Continuing to simplify:
Area = ½ * |(-24 + 60 - 42)|

Calculating the final result:
Area = ½ * |(-24 + 60 - 42)|
= ½ * |-6|
= ½ * 6
= 3

Therefore, the area of the triangle with vertices (-4, 0), (-10, 0), and (-7, -6) is 3 square units.