Q. 4 - 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 (5,1).
2. The lengths of the legs are 5 and 3.
3. The length of the segment is .

a. Step-1 – Given

The given points are (0,1) and (5,4). 

Step-2 – To determine

We have to find the coordinate of T.

Step-3 – Calculation

The point T lies on the horizontal line of (0,1). So, it’s y-coordinate = 1.

The point T lies on the vertical line of (5,4). So, it’s x-coordinate = 5.

So, the coordinate of T is (5,1).

b. Step-1 – Given

The given points are (0,1) and (5,4). 

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 (0, 1) and (5,1). So, the length = 5 – 0 = 5.

The length of the vertical leg is the distance between (5,4) and (5,1). So, the length = 4 – 1 = 3.

Hence, the lengths of the legs are 5 and 3.

c. Step-1 – Given

The given points are (0,1) and (5,4). 

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 (5, 4) and (0, 1).

$\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(5-0\right)}^2+{\left(4-1\right)}^2}\\ d=\sqrt{{\left(5\right)}^2+{\left(3\right)}^2}\\ d=\sqrt{25+9}\\ d=\sqrt{34}\end{array}$

So, the length of the segment is $\sqrt{34}$.