And this time, as we’re working with an area, then our units will be area units. Therefore, in order to find the area, we would take our length and width of 12 and five and multiply them together, which gives us a value of 60. In a similar way, we can look at the length of the line segment ?? and observe that it goes from zero on the ?-axis to five on the ?-axis, which means that the line segment ?? must be five units long. Earlier in the question, we established that ?? must be 12 units long as ? lies at 12 on the ?-axis and ? lies at zero on the ?-axis. We should remember that to find the area of a rectangle, we multiply the length by the width. Next, let’s see how we can find the area of this rectangle. Therefore, we’ve found our first answer that the length of line segment ?? would be 13 length units. Even though we’ve done some squaring, we’re not finding an area, so the units here will be length units. Finding the square root of 169 would give us a value of 13. So adding these together would give us 169.
Negative 12 squared will give us 144, and five squared gives us 25.
Simplifying this, we have the square root of negative 12 squared plus five squared. So plugging these into the formula would give us ? equals the square root of zero minus 12 squared plus five minus zero squared. But it doesn’t matter which way round we write these just so long as we take consistently from each coordinate. We can make ? our ? one, ? one values and ? our ? two, ? two values. This tells us that, for any pair of coordinates, ? one, ? one and ? two, ? two, the distance can be found by the square root of ? two minus ? one all squared plus ? two minus ? one all squared. This is the diagonal of the rectangle going from ? to ?.Īs we know the coordinate values for vertices ? and ?, we can recall the formula for the distance between two points. Now that we’ve found the coordinate values of all four vertices, let’s see if we can find the length of this line segment ??. So the coordinate of ? must be zero, five. Therefore, the ?-coordinate will be zero, and the ?-value will be the same as that of ?. We can alternatively think of this that the line segment ?? must be 12 units long. We can see that point ? sits on the ?-axis, so the ?-value will be zero. We know that ? lies at 12 on the ?-axis, and therefore ? must also lie at 12 on the ?-axis. So let’s look at this vertex ? in relation to ?. And we can be sure that ?? and ?? will be vertical lines. So we’ll have right angles at angles ?, ?, ?, and ?. We must remember that the definition of a rectangle is that all interior angles are 90 degrees. And so the line ?? must also be a horizontal line. We know that the line ?? lies on the ?-axis, which is a horizontal line. This other important piece of information that ? is at 12, five will help us work out the coordinates of vertices ? and ?. So in order to answer this question, we’ll need to look a little bit more closely at the vertices.įirstly, this vertex of ? must be the coordinate or ordered pair of zero, zero. We might notice that we’re not given any lengths in this diagram. In this question, we can see this rectangle ???? and we need to find a length and the area.
Given that ???? is a rectangle, find the length of line segment ?? and the area of the rectangle.