Q. 6 - Geometry

Question

In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

Step-by-Step Solution

Answer

1. The coordinate of T is (5,2).
2. The lengths of the legs are 4 and 3.

      3.    The length of the segment is 5.

a. Step-1 – Given

The given points are (1,2) and (5,5). 

Step-2 – To determine

We have to find the coordinate of T.

Step-3 – Calculation

The point T lies on the horizontal line of (1,2). So, it’s y-coordinate = 2.

The point T lies on the vertical line of (5,5). So, it’s x-coordinate = 5.

So, the coordinate of T is (5,2).

b. Step-1 – Given

The given points are (1,2) and (5,5).

Step-2 – To determine

We have to find the length of the legs of the right triangle.

Step-3 – Calculation

The length of the horizontal leg is the distance between (1,2) and (5,2). So, the length = 5 – 1 = 4.

The length of the vertical leg is the distance between (5,2) and (5,5). So, the length = 5 – 2 = 3.

Hence, the lengths of the legs are 4 and 3.

c. Step-1 – Given

The given points are (1,2) and (5,5). 

Step-2 – To determine

We have to find the length of the shown segment.

Step-3 – Calculation

We will use the distance formula to find the distance between (1,2) and (5,5).

$\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(5-1\right)}^2+{\left(5-2\right)}^2}\\ d=\sqrt{{\left(4\right)}^2+{\left(3\right)}^2}\\ d=\sqrt{16+9}\\ d=\sqrt{25}\\ d=5\end{array}$

So, the length of the segment is 5.