Question

finding distance on the coordinate plane

1. plot the points
2. create a triangle
3. find the distance between the points

point a (-4, 1) point b (2, 4)
point c (-5, 2) point d (-2, -4)
point e (3,1) point f (2, -3)
point g (2,-2) point h (3, -4)

Explanation:

Step1: Calculate horizontal/vertical differences

For points $(x_1,y_1)$ and $(x_2,y_2)$, compute $\Delta x = |x_1-x_2|$, $\Delta y = |y_1-y_2|$

Step2: Apply distance formula

Use $d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$, simplify or approximate.

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For Point C(-5,2) & Point D(-2,-4):

Step1: Compute coordinate differences

$\Delta x = |-5 - (-2)| = 3$, $\Delta y = |2 - (-4)| = 6$

Step2: Calculate distance

$d = \sqrt{3^2 + 6^2} = \sqrt{9+36} = \sqrt{45} = 3\sqrt{5} \approx 6.7$

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For Point E(3,1) & Point F(2,-3):

Step1: Compute coordinate differences

$\Delta x = |3 - 2| = 1$, $\Delta y = |1 - (-3)| = 4$

Step2: Calculate distance

$d = \sqrt{1^2 + 4^2} = \sqrt{1+16} = \sqrt{17} \approx 4.1$

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For Point G(2,-2) & Point H(3,-4):

Step1: Compute coordinate differences

$\Delta x = |2 - 3| = 1$, $\Delta y = |-2 - (-4)| = 2$

Step2: Calculate distance

$d = \sqrt{1^2 + 2^2} = \sqrt{1+4} = \sqrt{5} \approx 2.2$

Answer:

• Distance between C and D: $3\sqrt{5}$ (≈6.7)
• Distance between E and F: $\sqrt{17}$ (≈4.1)
• Distance between G and H: $\sqrt{5}$ (≈2.2)