Question

1. determine the length of straight line ab, where point a has xy coordinates (15, 10) and point b has coordinates (60, 70).

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Here, \( x_1 = 15,y_1 = 10,x_2=60,y_2 = 70 \).

Step2: Calculate differences in coordinates

First, find \( x_2 - x_1=60 - 15 = 45 \) and \( y_2 - y_1=70 - 10 = 60 \).

Step3: Square the differences

Square the results: \( (x_2 - x_1)^2=45^2 = 2025 \) and \( (y_2 - y_1)^2=60^2=3600 \).

Step4: Sum the squares

Add the squared values: \( 2025+3600 = 5625 \).

Step5: Take the square root

Take the square root of the sum: \( d=\sqrt{5625}=75 \).

Answer:

75