Find the area of the triangle with vertices: Q(-5,5,-3), R(-6,8,-4), S(-8,2,-4).

3.16 square units

Step-by-step explanation:

Find the area of the triangle with vertices: Q(-5,5,-3), R(-6,8,-4), S(-8,2,-4).

Step 1

We find QR and QS

QR = R - Q

= R(-6,8,-4) - Q(-5,5,-3)

= (-1, 3, -1)

QS = S - Q

= S(-8,2,-4) - Q(-5,5,-3)

= (-3, -3, -1)

Step 2

QR × QS

(-1, 3, -1) × (-3, -3, -1)

Using the formula:

a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k

Where a = (a1, a2, a3)

b = (b1, b2, b3)

QR = a

QS = b

(-1, 3, -1) × (-3, -3, -1)

a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k

= ((3 × -1) – (-1×-3))i + ((-1)×-3) – (-1) × -1)j + (-1 × -3) – (3×-3)k

= (-3 - 3)i + (3 – 1)j + (3 – 9)k

= 0i + 2j - 6k = (0,2,-6)

QR × QS = (0,2,-6)

Area of the triangle = √0² + 2² + 6²/ 2

= √0 + 4 + 36/2

= √40/2

= 6.324555320336759 /2

3.1622776602 square units

Approximately = 3.16 square units

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2