Q. 5 - 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 (7,2).
2. The lengths of the legs are 8 and 3.
3. The length of the segment is$\sqrt{73}$ .

a. Step-1 – Given

The given points are (-1,2) and (7,5). 

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 (7,5). So, it’s x-coordinate = 7.

So, the coordinate of T is (7,2).

b. Step-1 – Given

The given points are (-1,2) and (7,5).

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 (7,2). So, the length = 7 – (-1) = 7 + 1 = 8.

The length of the vertical leg is the distance between (7,2) and (7,5). So, the length = 5 – 2 = 3.

Hence, the lengths of the legs are 8 and 3.

c. Step-1 – Given

The given points are (-1,2) and (7,5). 

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 (7,5).

$\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(7-\left(-1\right)\right)}^2+{\left(5-2\right)}^2}\\ d=\sqrt{{\left(7+1\right)}^2+{\left(3\right)}^2}\\ d=\sqrt{{\left(8\right)}^2+{\left(3\right)}^2}\\ d=\sqrt{64+9}\\ d=\sqrt{73}\end{array}$

So, the length of the segment is $\sqrt{73}$.