Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = −1. If the area of ΔABC is 6 square units, then find a possible y-coordinate of point C. A: 6
B: 7
C: 8

A.  6

Step-by-step explanation:

Segment AB is on the line y = 2 and is 3 units long.

Point C is on the line x = −1.

FIND:

If the area of ΔABC is 6 square units, then find a possible y-coordinate of point C.

SOLUTION:

Area of a triangle = 1/2 b * h

segment AB is a horizontal line

the base of our triangle and point C is somewhere on the height.

If we can find the height of the triangle, we can add or subtract that height from y = 2 to get the possible y coordinate of point C.

We know that the x coordinate is -1 so,

6 = 1/2 (3) h

12 = 3h

h = 4

we can either add 4 or subtract 4 to the y coordinate of 2 to get the possible y coordinate of point C.

option 1

2 + 4 = 6 so the coordinate for C could be (-1, 6) or

option 2

2 - 4 = -2 so the coordinate for C could also be (-1, -2).

Since -2 is not in our choices but 6.

therefore,

the answer would be A. 6

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form