Triangle TUV, with vertices T(7,-9), U(9,-3), and V(3,-2), is drawn inside a rectangle, as shown below.What is the area, in square units, of triangle TUV?
To find the area of triangle TUV, we can use the formula for the area of a triangle when the coordinates of the vertices are known.
The formula for the area of a triangle with vertices at coordinates (x1, y1), (x2, y2), and (x3, y3) is given by:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Plugging in the coordinates of T(7,-9), U(9,-3), and V(3,-2) into the formula, we get:
Area = 1/2 * |7(-3 -(-2)) + 9(-2 -(-9)) + 3(-9 -(-3))|
Area = 1/2 * |7(-1) + 9(7) + 3(-6)|
Area = 1/2 * |-7 + 63 - 18|
Area = 1/2 * 38
Area = 19 square units
Therefore, the area of triangle TUV is 19 square units.
THAT ISNT THE RIGHT ANSWER BOT
I apologize for the mistake. Let's correct it.
To find the area of triangle TUV, we can use the formula for the area of a triangle given the coordinates of the vertices using the Shoelace Formula.
Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|
Substitute the coordinates of T(7,-9), U(9,-3), and V(3,-2) into the formula:
Area = 1/2 * |(7*(-3) + 9*(-2) + 3*(-9)) - ((-9*9) + (-3*3) + (-2*7))|
Area = 1/2 * |(-21 - 18 - 27) - (-81 - 9 - 14)|
Area = 1/2 * |-66 - (-104)|
Area = 1/2 * 38
Area = 19 square units
Therefore, the correct area of triangle TUV is 19 square units.
Triangle TUV, with vertices T(-5,5), U(-2,6), and V(-4,8), is drawn inside a rectangle, as shown below.What is the area, in square units, of triangle TUV?
To find the area of triangle TUV with vertices T(-5,5), U(-2,6), and V(-4,8), we will use the Shoelace formula.
The Shoelace formula for finding the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is:
Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|
Let's substitute the coordinates into the formula:
Area = 1/2 * |(-5*6 + (-2)*8 + (-4)*5) - (5*(-2) + 6*(-4) + 8*(-5))|
Area = 1/2 * |(-30 - 16 - 20) - (-10 - 24 - 40)|
Area = 1/2 * |-66 - (-74)|
Area = 1/2 * 8
Area = 4 square units
Therefore, the area of triangle TUV with vertices T(-5,5), U(-2,6), and V(-4,8) is 4 square units.
Triangle QRS, with vertices Q(3,3), R(9,2), and S(6,8), is drawn inside a rectangle, as shown below. What is the area, in square units, of triangle QRS?
To find the area of triangle QRS with vertices Q(3,3), R(9,2), and S(6,8), we will use the Shoelace formula.
The Shoelace formula for finding the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is:
Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|
Let's substitute the coordinates into the formula:
Area = 1/2 * |(3*2 + 9*8 + 6*3) - (3*9 + 2*6 + 8*3)|
Area = 1/2 * |(6 + 72 + 18) - (27 + 12 + 24)|
Area = 1/2 * |96 - 63|
Area = 1/2 * 33
Area = 16.5 square units
Therefore, the area of triangle QRS with vertices Q(3,3), R(9,2), and S(6,8) is 16.5 square units.
THAT ISNT THE RIGHT ANSWER
I apologize for the error. Let's correct it.
To find the area of triangle QRS with vertices Q(3,3), R(9,2), and S(6,8), we can use the Shoelace Formula.
Area = 1/2 * |(3*2 + 9*8 + 6*3) - (3*9 + 2*6 + 8*3)|
Area = 1/2 * |6 + 72 + 18 - 27 - 12 - 24|
Area = 1/2 * |96 - 63|
Area = 1/2 * 33
Area = 16.5 square units
Therefore, the area of triangle QRS with vertices Q(3,3), R(9,2), and S(6,8) is 16.5 square units.