Question

Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 6 units long. Point C is on the line x = −3. If the area of ΔABC is 9 square units, then find a possible y-coordinate of point C.

Answer 1

Answer:

y-coordinate is 5 or -1.

Step-by-step explanation:

Point A is at (x, 2) and B is at (x+6, 2). Since AB must lie on the line y=2  and be 6 units long. Point C is on the line x = -3 . So let C be at (-3, y).

Since ΔABC is a right angle, then point C must have the same x-coordinate as point A. Therefore, A(-3, 2) and B(2, 2).

The area of ΔABC is 6. So,

9 = 1/2 (b)(h)

where b is the base and h is the height.

so b = 6 and h = AC

Solving this for C gives

9 = 1/2 (6)(AC)

18/6 = AC

3 = AC

9 = 1/2 (6)(AC)

18/6 = AC

3 = AC

Point C must lie 3 units above point A or 3 units below the point A. If it lies 3 units above, then it has a y-coordinate of 2 + 3 = 5.

If it lies 3 units below, it has a y-coordinate 2 - 3 = -1.

Therefore, y-coordinate is 5 or -1.

Answer 2

The possible value of y-coordinate of the point C will be 5 or -1.

Given information:

Right triangle ABC is on a coordinate plane.

Segment AB is on the line y = 2 and is 6 units long.

Point C is on the line x=−3.

The area of triangle ABC is 9 square units.

AB is on the line y=2 which is parallel to the x-axis. So, AB will be parallel to x-axis.

Point C is on the line $x=-3$ which is parallel to y-axis. So, side BC or AC will be parallel to y-axis.

So, AB will be perpendicular to the other side containing point C (BC or AC). From this, the y-coordinate of the point C should be such that the length of the side or leg containing C should justify the area of the triangle.

The length of other leg of the triangle should be,

$\rm BC\; or\; AC=\dfrac{9}{3}\\=3$

So, the y-coordinate of the point C can be,

$2\pm3=5,-1$

Therefore, the possible value of y-coordinate of the point C will be 5 or -1.

For more details, refer to the link:

https://brainly.com/question/17727748