Question

18
point h is located at (3.5, -2). which two points are located at a distance of 2.5 units from point h?
point i
point j
point k
point l
point m

Explanation:

Step1: Identify coordinates of all points

Point $H=(3.5, -2)$, $I=(-1, 1)$, $J=(1, 3.5)$, $K=(1, -2)$, $L=(3.5, 0)$, $M=(3.5, -4.5)$

Step2: Use distance formula for each point

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

• For $H$ and $I$: $d=\sqrt{(3.5-(-1))^2+(-2-1)^2}=\sqrt{4.5^2+(-3)^2}=\sqrt{20.25+9}=\sqrt{29.25}\approx5.41$
• For $H$ and $J$: $d=\sqrt{(3.5-1)^2+(-2-3.5)^2}=\sqrt{2.5^2+(-5.5)^2}=\sqrt{6.25+30.25}=\sqrt{36.5}\approx6.04$
• For $H$ and $K$: $d=\sqrt{(3.5-1)^2+(-2-(-2))^2}=\sqrt{2.5^2+0^2}=2.5$
• For $H$ and $L$: $d=\sqrt{(3.5-3.5)^2+(-2-0)^2}=\sqrt{0^2+(-2)^2}=2$
• For $H$ and $M$: $d=\sqrt{(3.5-3.5)^2+(-2-(-4.5))^2}=\sqrt{0^2+2.5^2}=2.5$

Answer:

Point K, Point M