Question

the height of this isosceles triangle is twice the length of its base. what are the coordinates of the undefined vertex?

Answer 1

Height is 2x length of base. What is the distance between (10,0) and (4,0)?

Answer 2

And what is the midpoint between (10,0) and (4,0)?

Answer 3

6

Answer 4

Okay, that's the distance between them, what's the midpoint?

Answer 5

3

Answer 6

so the answer is 3?

Answer 7

Mmm, that's the distance to the midpoint, but what's the actual location of the midpoint?

Answer 8

in the middle

Answer 9

What are the coordinates of that point?

Answer 10

the y-value is obviously 0. what's the x-value?

Answer 11

10 and 4?

Answer 12

What is the midpoint between (4,0) and (10,0)? Remember, the midpoint is the average of the corresponding values. (average of 4,10 is x value, average of 0,0 is y value)

Answer 13

7

Answer 14

No, it's (7,0). The difference is important.

Answer 15

Okay, we decided that the length of the base was 6 (10-4). The height of this triangle is twice the length of the base, so what will the height be?

Answer 16

112

Answer 17

112?

Answer 18

2*6 = 12

So the height is 12. We know that one base corner is at (4,0), and the other base corner is at (10,0). We found the midpoint of the base to be (7,0). The height of the triangle is 12. Given that the vertex of the triangle is over the midpoint of the base, and is 12 above the base, what are the coordinates of the vertex?

Answer 19

7,12

Answer 20

Yes!

Answer 21

(7,12) is the right answer.