Question

q1 - accelerated mathematics gr 8 | lesson: solving real problems involving distance
target due: monday
for the points (1, 1) and (1, 4), what is the distance?
a. 5
b. 9
c. 3
d. 7
for points (2, 3) and (6, 7), what is the calculated distance?
a. 5
b. √20
c. 6
d. √32

Explanation:

Step1: Recall distance formula

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

Step2: Solve first problem

For points $(1,1)$ and $(1,4)$, $x_1 = 1,y_1 = 1,x_2 = 1,y_2 = 4$. Substitute into formula: $d=\sqrt{(1 - 1)^2+(4 - 1)^2}=\sqrt{0 + 9}=3$.

Step3: Solve second problem

For points $(2,3)$ and $(6,7)$, $x_1 = 2,y_1 = 3,x_2 = 6,y_2 = 7$. Substitute into formula: $d=\sqrt{(6 - 2)^2+(7 - 3)^2}=\sqrt{4^2+4^2}=\sqrt{16 + 16}=\sqrt{32}$.

Answer:

For the first question: c. 3
For the second question: d. $\sqrt{32}$