Question

find distances between ordered pairs, limited to either the same x - coordinate or y - coordinate given ordered pairs that are: integers, decimals or fractions in different quadrants (l4)
find the distance, in units, between point t (4, 7) and point s (4, - 3).
find the distance, in units, between point p (- 6, 5) and point u (3, 5).

Explanation:

First Sub - Question (Distance between T(4, 7) and S(4, - 3))

Step1: Identify the formula

When two points \((x_1,y_1)\) and \((x_2,y_2)\) have the same \(x\) - coordinate (\(x_1 = x_2\)), the distance \(d\) between them is given by \(d=\vert y_1 - y_2\vert\). Here, \(x_1=x_2 = 4\), \(y_1 = 7\) and \(y_2=-3\).

Step2: Substitute the values

Substitute \(y_1 = 7\) and \(y_2=-3\) into the formula \(d=\vert y_1 - y_2\vert\). We get \(d=\vert7-(-3)\vert=\vert7 + 3\vert=\vert10\vert = 10\).

Second Sub - Question (Distance between P(-6, 5) and U(3, 5))

Step1: Identify the formula

When two points \((x_1,y_1)\) and \((x_2,y_2)\) have the same \(y\) - coordinate (\(y_1 = y_2\)), the distance \(d\) between them is given by \(d=\vert x_1 - x_2\vert\). Here, \(y_1=y_2 = 5\), \(x_1=-6\) and \(x_2 = 3\).

Step2: Substitute the values

Substitute \(x_1=-6\) and \(x_2 = 3\) into the formula \(d=\vert x_1 - x_2\vert\). We get \(d=\vert-6 - 3\vert=\vert-9\vert=9\).

Answer:

• Distance between T(4, 7) and S(4, - 3): \(10\)
• Distance between P(-6, 5) and U(3, 5): \(9\)