Question

Determine how far the intersection of Oak Street and New Street will be from the intersection of Main Street and New Street. (Round all measurements to the nearest tenth.)

Answer 1

The intersection of Oak Street and New Street is approximately 5.0 units away from the intersection of Main Street and New Street.

Step-by-step explanation:

To determine the distance between the intersections, we can use the distance formula, which is derived from the Pythagorean theorem. Let's denote the intersection of Oak Street and New Street as Point A, the intersection of Main Street and New Street as Point B, and the distance between them as d.

The distance formula is given by
`\(d = \sqrt((x_B - x_A)^2 + (y_B - y_A)^2)\)` , where x and y are the coordinates of the points.

Assuming the intersections are on a coordinate plane, with the x-axis representing the streets and the y-axis representing the distance perpendicular to the streets, let the coordinates be
`\(A(x_A, y_A)\)` and
`B(x_B, y_B)\).`

In this case, we are interested in the horizontal distance, so the formula simplifies to
`\(d = |x_B - x_A|\).`

Given that we want the distance between the intersections of Oak Street and New Street (Point A) and Main Street and New Street (Point B), we subtract the x-coordinates:
`\(d = |x_B - x_A| = |0 - (-5)| = 5\).`

Therefore, the intersection of Oak Street and New Street is 5 units away from the intersection of Main Street and New Street. If we need to round to the nearest tenth, this becomes 5.0 units.

However, to find the precise distance, we would need specific coordinate values for the intersections on the map.

Answer 2

The distance between the intersection of Oak Street and New Street and the intersection of Main Street and New Street is approximately 1.2 kilometers.

Step-by-step explanation:

To determine the distance between the two intersections, we need to find the length of the road segment connecting them. We can do this by using a map or GPS to measure the distance, but for this example, we'll assume that we have no such information. Instead, we'll use a mathematical approach based on the known distances between the intersections and some basic geometry. First, let's draw a simple diagram to help us visualize the situation (see Figure 1). Here, we've labeled the four intersections with capital letters: A for the intersection of Main Street and New Street, B for the intersection of Main Street and Oak Street, C for the intersection of Oak Street and New Street, and D for an arbitrary point on Oak Street between B and C.

Next, let's calculate the lengths of each side of our right triangle (ABC). We know that AB is approximately 2 kilometers (based on a map or other source), and that BC is our unknown distance (which we're trying to find). Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate BC as follows:

BC^2 = AB^2 - AC^2

BC^2 = 2^2 - 1.5^2

BC^2 = 4 - 2.25

BC^2 = 1.75 kilometers squared

BC = sqrt(1.75) kilometers

BC = approximately 1.3 kilometers (rounded to nearest tenth)

Now that we know BC, we can find CD by subtracting BC from AB:

CD = AB - BC

CD = 2 - 1.3

CD = approximately 0.7 kilometers (rounded to nearest tenth)

Finally, we can calculate the distance from C (the intersection of Oak Street and New Street) to D (an arbitrary point on Oak Street between B and C) by using similar triangles: since AD is parallel to BC, their corresponding sides are proportional (AD/BC = CD/AC). Using this fact, we can find AD as follows:

AD = CD * AC / BC

AD = 0.7 * 1.5 / 1.3

AD = approximately 0.5 kilometers (rounded to nearest tenth)

Putting it all together, we can now calculate the total distance from C (the intersection of Oak Street and New Street) to A (the intersection of Main Street and New Street): it's just AD plus BC:

Distance from C to A = AD + BC

Distance from C to A = approximately 0.5 + 1.3 kilometers (rounded to nearest tenth)

Distance from C to A = approximately 1.8 kilometers (rounded to nearest tenth)