Video Transcript
Given that 𝐴𝐵𝐶 is an isosceles
triangle, where the coordinates of the points 𝐴, 𝐵, and 𝐶 are eight, negative
two; negative two, negative two; and zero, negative eight. Find the area of triangle
𝐴𝐵𝐶.
So to help us understand what’s
going on in this question, I’ve drawn a sketch. So I’ve got the points 𝐴, 𝐵, and
𝐶. And I’ve joined them to make a
triangle. And I’ve also shown that the
triangle is an isosceles triangle. And so I have marked that on. And we can see that because as
we’re told that it’s an isosceles triangle and we can clearly see that the line 𝐵𝐶
is shorter than the other two, then the other two lines must be the same because, as
we know, it’s an isosceles triangle.
So now to solve the problem, what
we’re gonna do is work out the area of the triangle. And to do that we have a
formula. And that formula states that the
area of a triangle is equal to half the base times the height where the height is
the perpendicular height. And what we mean by perpendicular
height is the height at right angles to the base.
So the first thing we need to do to
work out the area of the triangle is work out the length of our base, so 𝐵. 𝐵 is gonna be equal to eight,
because that’s the 𝑥-coordinate of point 𝐴, minus negative two, because that’s the
𝑥-coordinate of point 𝐵, which is gonna give us a result of 10. And that’s because if you subtract
a negative it’s the same as add. So eight add two is 10. And if we think about a number line
if we’re counting up from negative two to eight, we count up 10 steps. So this is correct. So great, that’s our length of our
base.
So now, what we want to do is work
our perpendicular height ℎ. And to do this, this is gonna be
equal to negative two minus negative eight. And that’s because we’ve got
negative two because that’s the point at which 𝐴𝐵 crosses the 𝑦-axis. And then we subtract from this
negative eight. And that’s because negative eight
is the 𝑦-coordinate of point 𝐶. Again, when you subtract a negative
it’s positive. So you have negative two add eight
which gives a six. And again, if we think about if
we’re counting down from negative two to negative eight, it would be six spaces or
six units. So that’s correct.
So we’ve got our 𝐵 and our ℎ. So now, let’s find the area of our
triangle. So, therefore, the area of the
triangle 𝐴𝐵𝐶 is gonna be equal to a half multiplied by 10 multiplied by six. And we can work this out by
thinking, what is half of 10? Well, it’s five. Five multiplied by six is 30. So, therefore, we can say that the
area of the triangle 𝐴𝐵𝐶 — given that the coordinates of the points 𝐴, 𝐵, and
𝐶 are eight, negative two; negative two, negative two; and zero, negative eight —
is 30 units squared. And that’s our area.
