Question

1. (-5, 1) and (-5, 7) 20) (-9, 6) and (-3, 2)

Explanation:

Problem 19: Distance between \((-5, 1)\) and \((-5, 7)\)

Step 1: Identify the formula for vertical distance

Since the \(x\)-coordinates are the same (\(-5\)), the distance is the absolute difference of the \(y\)-coordinates. The formula for distance between \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1 = x_2\) is \(|y_2 - y_1|\).

Step 2: Substitute the values

Here, \(y_1 = 1\) and \(y_2 = 7\). So, distance \(=|7 - 1|=|6| = 6\).

Problem 20: Distance between \((-9, 6)\) and \((-3, 2)\)

Step 1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step 2: Substitute the values

Here, \(x_1=-9,y_1 = 6,x_2=-3,y_2 = 2\).
First, calculate \((x_2 - x_1)=-3-(-9)=-3 + 9=6\).
Then, calculate \((y_2 - y_1)=2 - 6=-4\).
Now, substitute into the formula: \(d=\sqrt{(6)^2+(-4)^2}=\sqrt{36 + 16}=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx 7.21\) (if decimal approximation is needed).

Answer:

s:

1. The distance is \(\boldsymbol{6}\).
2. The distance is \(\boldsymbol{2\sqrt{13}}\) (or approximately \(\boldsymbol{7.21}\)).