Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?
a. (5,6)
b. (6,6)
c. (-5,1)
d. (-4,1)

Question

Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?
a. (5,6)
b. (6,6)
c. (-5,1)
d. (-4,1)

calculusxy · Answer

@amistre64

calculusxy · Answer

Is it (5,6)?

amistre64 · Answer

hm, 01 and 06 are both in the y axis so im assuming its a height ... a height of 5

we are given the 5b/2 = 10 to determine a base value with;  what is b?

calculusxy · Answer

4 right because 5*4=20 and then divided by 2 equals to 10

amistre64 · Answer

yep, so my guess is that x will have a 4 in it ... +or-,  and have a y value that is the same as one of the given points

amistre64 · Answer

as such, we can try out the options,  since the x values give us base lengths

distance is always a positive value so we should wrap the x parts in absolute value signs

5*|5|/2 = 10?
5*|6|/2 = 10?
5*|-5|/2 = 10?
5*|-4|/2 = 10?

calculusxy · Answer

so is it (-4,1)? @amistre64

amistre64 · Answer

thats the one i would pick yes :)

calculusxy · Answer

Thanks :)