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Math  /  Geometry

Question1) S4 A\mathrm{S}^{4} \mathrm{~A} Find the distance between the points (−3,−5)(-3,-5) and (7,10)(7,10). [x] Round decimals to the nearest tenth. [a] □\square units

Studdy Solution

STEP 1

1. We are using the Cartesian coordinate system.
2. The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in the plane is calculated using the distance formula.
3. The final answer should be rounded to the nearest tenth.

STEP 2

1. Recall the distance formula.
2. Substitute the coordinates of the given points into the formula.
3. Simplify the expression under the square root.
4. Calculate the square root and round to the nearest tenth.

STEP 3

Recall the distance formula for two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

STEP 4

Substitute the coordinates of the points (−3,−5)(-3, -5) and (7,10)(7, 10) into the formula:
d=(7−(−3))2+(10−(−5))2 d = \sqrt{(7 - (-3))^2 + (10 - (-5))^2}

STEP 5

Simplify the expression under the square root:
d=(7+3)2+(10+5)2 d = \sqrt{(7 + 3)^2 + (10 + 5)^2} =102+152 = \sqrt{10^2 + 15^2} =100+225 = \sqrt{100 + 225} =325 = \sqrt{325}

STEP 6

Calculate the square root and round to the nearest tenth:
d≈325≈18.0 d \approx \sqrt{325} \approx 18.0
The distance between the points is:
18.0 units \boxed{18.0 \text{ units}}

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