Answer:
PQ = 5 units
QR = 8 units
Step-by-step explanation:
Given
P(-3, 3)
Q(2, 3)
R(2, -5)
To determine
The length of the segment PQ
The length of the segment QR
Determining the length of the segment PQ
From the figure, it is clear that P(-3, 3) and Q(2, 3) lies on a horizontal line. So, all we need is to count the horizontal units between them to determine the length of the segments P and Q.
so
P(-3, 3), Q(2, 3)
PQ = 2 - (-3)
PQ = 2+3
PQ = 5 units
Therefore, the length of the segment PQ = 5 units
Determining the length of the segment QR
Q(2, 3), R(2, -5)
(x₁, y₁) = (2, 3)
(x₂, y₂) = (2, -5)
The length between the segment QR is:
[tex]l=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(2-2\right)^2+\left(-5-3\right)^2}[/tex]
[tex]=\sqrt{0+8^2}[/tex]
[tex]=\sqrt{8^2}[/tex]
Apply radical rule: [tex]\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]=8[/tex]
Therefore, the length between the segment QR is: 8 units
Summary:
PQ = 5 units
QR = 8 units
