Video Transcript
Use the graph below to determine the coordinates of the points 𝐴, 𝐵, and 𝐶; then find the area of the resulting figure from connecting the points.
So the first part of this question, it actually asks us to determine the coordinates of our points 𝐴, 𝐵, and 𝐶. So let’s do that first. Well, whenever we’re reading a coordinate, the first number is always the 𝑥-coordinate and the second number is the 𝑦-coordinate. Sometimes people know this as along the corridor and up and down the stairs. So therefore, for our point 𝐴, the coordinate is going to be negative two, zero. And that’s cause we can see that it’s negative two on the 𝑥-axis and then zero on the 𝑦-axis because it’s, in fact, on the 𝑥-axis, which is the zero point of our 𝑦-axis.
And then for point 𝐵, we’re gonna have negative two, five. And we get this because the 𝑥-coordinate is negative two. And then the 𝑦-coordinate is five. So then our final coordinate is 𝐶, and that’s two, five. So therefore, we can say the coordinates of our points 𝐴, 𝐵, and 𝐶 are negative two, zero, negative two, five, and two, five, respectively. Okay, great. So that’s the first part of our question answered. Now, let’s move on to the second part.
So in the second part of this question, what we’re looking to do is find the area of the resulting figure from connecting our points. So what’s the first thing we need to do? Let’s connect the points. So when we connect our points, we can see that it makes a right triangle. And we have a formula for the area of a triangle. And that is that it’s equal to a half 𝑏ℎ, where 𝑏 is the base and ℎ is the height. And this is, in fact, the perpendicular height. So what this means is that it’s at right angle to the base. So in our triangle, we can see that 𝐵𝐶 is gonna be our base and 𝐵𝐴 is gonna be our height.
And we can see the base is equal to four units. That’s because if we count across our axis, we can see that it is four units. But also, we could have worked this out by subtracting the 𝑥-coordinate of 𝐵 from the 𝑥-coordinate of 𝐶. So that would be two minus negative two. Well, if we subtract a negative, what we have is the same as adding a positive. So this gives us four. And similarly, if you want to find the height, this can be equal to five units and that’s because what we do is subtract the 𝑦-coordinate of 𝐴 away from the 𝑦-coordinate of 𝐵, so five minus zero, which equals five.
So therefore, we now have our base and our height. So what we can do is work out the area. So this is gonna be equal to a half multiplied by four multiplied by five, which is gonna be equal to two multiplied by five, which is gonna give us our final answer of 10 area units.
